Let's discuss the issues in moves and why things are getting better.

Also known as "Here I justify my big rebuff debuff list" and "Here I vent off some more steam about balance".

Part a. Distribution Methods:

Part i. Technical Machines:

Ever since the inception of the series, the Technical Machines remained as the best distribution method in the game. Not only most the best moves of the game were available through Technical Machines, the moves also had the best distribution compared to any other move. However, as generations continued on, some issues started to emerge:

1. From the transition to Gen II from Gen I and from Gen IV to Gen V, the quality of TM moves have diminished. Notable moves such as Avalanche and Dark Pulse were switched out for the likes of Struggle Bug(which was really powerless in Gen V). While Gen VI largely fixed that, some issues still remain. Such as:
2. The new TMs have very terrible distributions. This was not the case for Gen IV, but for later generations, even the older moves started to get low distribution. For example, Swords Dance used to be available for most Grass-types, but currently only so few of the new Grass-types actually learn it. Similarly, Quash and Sky Drop, which were introduced in Gen V, are infamous for their low distribution. Dazzling Gleam is also largely exclusive to some Grass and Psychic-types with very few Ghost-types, which is pretty low compared to the likes of Heat Wave or Psychic. 
3. Many of the common TMs that were retconned out in Gen V returned as Egg Moves, but when they came back as TMs, not only they remained as Egg Moves,  For example, Roost and Sleep Talk remain as Egg Moves. Since they remained as Egg Moves, TMs are no longer passable. This artificially inflates the number of the Egg Moves, which were already inflated with the level-up moves of their Basic stages. Similarly, with this change in the mechanics of TMs, many TM moves were instantly justified to become Egg Moves to fill the shallowness of Gen VI Egg Moves, such as Thief for Klefki and Rock Polish for Tyrunt.
4. The TMs themselves are still in imbalance. There is no physical Ice TM, nor is there a physical Fairy TM. Similarly, there is no special Rock TM. Some of this are caused by the lack of variety in the types, for example there can't be another Status TM for Ice-type because there is Ice-type Status move that isn't Hail.
5. The TMs are artificially forced to stay around 100, when in terms of the TM to total move count ratio there should be around 150 now, as in Gen IV where the 100 rule was more or less established, there was around 400 moves, and similarly when there was around 150 moves, there was the first 50 TMs. Now there is around 600 moves, which would mean that there should be more moves. 

So, why are things getting better?

First of all, let's discuss the first issue. As I stated before, not only some of the common moves have returned, others have been buffed significantly, for example Struggle Bug was buffed to 50 BP, and Will-O-Wisp's accuracy was buffed from 75 to 85 from transition to Gen VI from Gen V, and Drain Punch/Giga Drain, who were Tutor moves in Gen V and TM in Gen IV were buffed to 75 BP/10 PP from 60 BP/5 PP in the transition from Gen IV to Gen V. This is because TM moves are high level moves with varying degrees of usability in the main story, but they have roughly similar competitive value. This has been the case since they were one-shot items, and it continues on ever since they become infinitely usable.

The second issue is harder to discuss. This is because of the new moveset distribution methods. Each Pokémon no longer gets a wide variety of moves that aren't their specialty. They either get moves that fit their highest attack stat or vice versa. There is almost in-between, even if there isn't a large difference between the stats. In addition, the forced division between each stage ensures that each stage will get at least one move exclusive to it, that won't be available for the pre-evolution for illogical reasons. Unless this ridiculous pragmatism is averted and Pokémon are given more access to alternate moves for sake of flavour's sake, and more moves that will make them actually good instead of going against their distribution, this issue will continue.

On the other hand, it is true that each new move gradually gets larger and larger distributions, and while the low Pokémon count will obviously continue, there has been more push towards retconning TM lists, whereas in the past they have been more or less final. While things are not looking any good, they are not cancerously awful, just diarrhea-inducingly awful.

The third issue is less important. The same thing happened with Gen IV moves. While it is true that former Move Tutor moves were retconned out of the Egg Moves, there were still TM moves that were obtained only through breeding. These were retconned out of the Egg Moves and brought into TMs. It is most likely that the current awkward situation was caused by the fact that X/Y had to be rushed out and because they wanted to justify Roggenrola's Rock Tomb Egg Move, and it is unlikely that this situation will be kept, unless they want to continue to enforce 100 TM nonsense.

The fourth issue is not an issue exclusive to TMs. We will discuss it in more detail as its own subsection.

The fifth issue really pisses me off. There are two reasons why this issue is not averted. First one is Move Tutors. TMs are castrated to ensure a healthy supply of Move Tutor moves, and they provide a justification for getting mid-generation games, which wouldn't sell well otherwise. The second issue is the game development confusion. High list of TMs means high list of high tier moves with high availability that requires massive amounts of balancing and rebalancing. Not only that, the high amount of TMs means more items have to be arranged and rearranged for each game. However, as stated before, this is not a large issue. There is already 600 something moves, and many of the moves have been ancient TMs that have not returned as Move Tutor moves, whereas others did, as such they already have an almost modern distribution. Not to mention, while 100 TM is forcefully enforced, the TM count has been increasing, just with baby steps.

On contrast, the issues regarding locations and item count are genuine. Unfortunately, there is little can be done to properly arrange TMs, as even in their current situation they are bit cumbersome. However, there are ways to cut down confusion with the locations, by shoehorning them into stores everywhere.

Part ii. Move Tutors:

Move Tutors had their humble beginning in Gen I, when Pikachu was given the opportunity to Surf. True Move Tutors have only been introduced in Crystal, however, as the elemental beams were replaced in favor of elemental punches, in Gold/Silver which were considerably weaker, though they granted a bit more variety. This standardized the tradition of lost TMs returning as Move Tutors. In FireRed and LeafGreen, XD and for some of the moves in Emerald, the Move Tutors have been one-shot methods much like TMs, but they couldn't be replenished. This was changed in Platinum with the introduction of the Shard system, and HeartGold/SoulSilver used BP system that originated in Emerald.

The second tradition of unique Move Tutors was a bit more awkward. While it started in the Stadium, when it returned in FR/LG, the elemental Hyper Beams were one-shot moves, whereas XD's Mew Tutors were obtained through PokéCoupons. By Diamond/Pearl, these elemental beams were made available for all starters alongside the newly introduced Draco Meteor tutor. This tradition continued with Pledge moves of Gen V and the legendary Tutors that originated there, and the introduction of new moves through exclusive Tutors pretty much died in Gen V, but Pledge Moves were buffed in Gen VI.

So history aside, what's the issue with Move Tutors? Well:

1. First and foremost, most of the Move Tutors that aren't former TMs have low distributions. Especially new moves like Dual Chop and Drill Run have really, really bad distributions.
2. The expansions of the Move Tutors are far more schizophrenic. It is more likely to see a low tier moves to disappear then to see them become improved upon. Rollout and Gen III Move Tutors are perhaps the most famous examples of these cases.
3. Move Tutors forcefully keep necessary archetypes for TMs as their hostage. The worst example of this would be the former TM Ice Punch, as it is the most common of the physical Ice-type moves, yet it is unavailable for most Pokémon without breeding until the mid-generation games.
4. The exclusive Move Tutors are really exclusive. None of them are given to any other Pokémon, even those that make sense like the new Mega Evolving not-quite-Dragon-type Pokémon, and the Elemental Monkeys.
5. The exclusive Move Tutors are not elaborated upon. In this generation, we haven't got any new exclusive Move Tutors.

So, why are things getting better?

Firstly, actually the first issue isn't getting better. It is actually getting worse.

You see, most of Move Tutor moves require the Pokémon to be a specific body type or elemental type. This cuts down the possible distribution of most moves, because how are you going to something that doesn't have hands Punching moves? In addition, ever since Gen IV, the Move Tutors have been the primary source of diversion between pre-evolutions and evolutions. There is no logical explanation as to why Gible can't learn Aqua Tail yet Garchomp can, and similarly there is no logical reason why Swinub can't learn Iron Head yet Mamoswine can.

In addition, from the generational transitions, several Move Tutors in several Pokémon's moveset were lost to the streams of time. The most infamous example would be Snore, as since Gen III it was eradicated from the movesets of Pokémon with sleep evading abilities, even if they had other abilities in the first place. This extends to less famous stuff, such as Thunder Wave on some Pokémon like Zangoose, and Qwilfish's Swords Dance. This is completely baffling, and absolutely absurd.

Of course, there is a remedy for this. Move Tutors are more flexible than TMs, as such, not only the list of moves that are available as Tutors are prone to change, Move Tutor lists themselves are very prone to retcons, as it is more justifiable why a man can't teach a Pokémon it should be able to learn, than why an optimized machine can't. In addition, since Move Tutors are just inter-generational additions, they are more open to freedom.

Another remedy is the Egg Moves. To make certain evolutions stronger, many Baby Pokémon gain Egg Moves of former Tutors that they couldn't learn initially. Most recent example for this would be Air Cutter on Charmender, but Drain Punch Shroomish is considerably more amusing. Unfortunately, these changes often don't reflect on the actual Move Tutor lists, as they are not really treated with care.

And while it is true that Move Tutors gain more distribution as the generations pass, as stated before, they are axed off and forgotten more easily then TMs.

Second issue also remains strong. While I strongly believe that Omega Ruby/Alpha Sapphire will bring back many moves that were lost to time, and the remakes of Diamond/Pearl will probably help restore balance of the metagame and history of the franchise, there is always a fear of the cost.

The third issue on the other hand is being fixed. As recently, the only good special Dark-type move Dark Pulse was brought back, alongside other necessary moves like Roost and Sleep Talk. While the current situation is still far from perfect, there is a much tighter sense of balance, and if the TM list ends up expanding  dramatically as it should have done in this generation, there will be less hostage moves. On the other hand, the existing Pokémon are also getting their Move Tutor moves from Egg Moves one by one, to the point that some of them actually only have around three Tutor exclusive moves. So things are not as dark for this specific issue.

However, this issue will still linger on, as there is no other incentive to but the mid-generation games, even though Mega Evolutions actually provide that incentive now.

The fourth issue is likely not going to be resolved any time soon. The exclusivity is still a strong aspect of the franchise, even when all Pokémon have evolved into drastically different creatures, and the starters have other exclusives like Mega Evolutions. While the issue regarding Draco Meteor will probably be resolved as we need Mega Evolutions to be instant win buttons, I mean, aces of their respective teams, the issue regarding other Starter Move Tutors, or even the ancient Mew Tutors of XD will likely not be addressed.

The fifth issue is probably not going to be fixed, considering the unpopularity of the said moves, except Secret Sword and Draco Meteor. Even though Pikachu would enjoy its own exclusive Tutors. Granted, we now have some alternate methods of giving Pokémon new moves like Cosplay Pikachu's costumes, but they aren't actually relevant.

Part iii. Egg Moves:

Existing only as recently of Gen II, Egg Moves have always provided Pokémon with moves that can't learn conventionally... for the most part. This moves have increased the usability of the Pokémon... of certain species. Of all of the methods presented, they are the third most convenient way of getting moves... if the Pokémon is in Field Egg Group or there aren't convoluted chains involved. Yeah... most of the time Egg Moves are not very good. Let's discuss why.

Traditionally, Egg Moves were not high tier moves, but rather mid-to-lower tier moves that were granted to Pokémon primarily for sake of flavour. Most other moves were also only available through transferred Gen I TMs. This was changed a bit with Crystal, with Crunch being granted for many Pokémon. But these two elements have been significant forces on Egg Moves.

Similarly, in Gen II, when the elemental beams were abolished from the TM list, they returned as Egg Moves for certain Pokémon, such as Thunderbolt on Mareep. This also helped to establish the standard of Move Tutor moves to be present in Egg Move lists.

However, two new issues have emerged with Generation VI. One of these was the aforementioned TM issue. The other one, which was actually older than Gen VI, but intensified in it, was the issue of level-up moves emerging Egg Move lists. Generally, this is not a bad thing. Some high level moves used to end up in Egg Moves for sake of convenience, like Superpower on Marill. Others were exclusive to their evolutions, like Flare Blitz on Charmender. However, in Gen VI, you see really pointless filler like Metal Sound on Honedge. Honedge can learn Metal Sound literally around Level 10s.

On the other hand, one can easily criticize high level moves' presence in Egg Moves, as if you have two parents that have Superpower, you will still gain Superpower on Marill regardless of whether it is an Egg Move or not, since that's how standard Level-Up moves pass on.

The biggest issue of Egg Moves is their complication, however. Certain moves like Air Cutter on Charmender and Defense Curl on Bagon are only available through ancient Move Tutors, and let's not get into the whole chain breeding examples.

So, are things getting better?

The TM issue will likely resolve itself, as discussed before.

As for the lack of power of the Egg Moves, as each generation expands upon most of the Pokémon species' Move rosters, this too is an issue that will resolve itself. Not to mention, as Egg Moves themselves contain a large variety of Tutor moves, other Egg Moves have to be improved upon to be as attractive as them, unless they are only granted for sake of flavour.

The issues of the complication is also an issue that will likely resolve itself. As Move Tutors return, the issue of ancient Tutors will likely get abolished. Similarly, as each Egg Group gets more varied Pokémon with more varied movesets, it will be easier for Egg chains to become smaller, if they don't simply stop existing.

Another "good" thing larger variety in Egg Groups brings is that there will more chains that will be established, as such Game Freak will likely grant more Egg Moves to force people into buying game guides. As it has been the case for any other generational shift Egg Move changes.

Part iv. Leveling Up:

The most basic method of move learning, leveling up is possibly the worst method of learning new moves. Here's why:

1. Level-up learnsets are incredibly unbalanced in terms of levels. Things are getting much better with each level-up moveset change in each game, however there are several archaic moves that are still considered to be "good", like the horrible Take Down.
2. The level-up learnsets, much like any other learnset, are more biased towards evolutions, and most evolutions are granted a few exclusive moves for their own... even if the exclusive moves don't make sense to be exclusive. Such as Heat Wave on Charizard and Iron Defense on Escavalier, both which are available to their pre-evolutions through Move Tutor.
3. Each Pokémon can only get around 10-25 moves from leveling up. Pre-evolutions get less.
4. There are often unnecessary repeats in learnsets. The most infamous one would be Trick-or-treat for Pumpkaboo/Gourgeist, which is really jarring as Gourgeist sucks because of its shallow movepool, rather than due to its stats or typing.
5. Most learnsets don't actually go to around 100s, and those that do usually have a new move in around every 10 levels.

While none of these issues will be completely fixed in the current system, learnsets are quite literally altered in each generation and once again in one or two of the intergenerational games. As such, while level-up moves have a lot of issues, the overall quality of the movesets is mostly steadily increasing. Unfortunately, many moves end up lost due these constant changes.

Part b. Distribution Biases:

Part i. Evolution bias:

As discussed before, the level-up moves are biased towards Evolved stages. Lower stages have generally less Level-Up moves. This means that whatever the pre-evolution will do, by the virtue of being pre-evolution they are doomed to have lower movesets than their evolutions.

Sometimes, this is reasonable, for example Prinplup and Empoleon both get Metal Claw because their wings contain claws, but Piplup doesn't. Similarly, Butterfree gets Air Cutter because it is Flying-type, while Weedle doesn't.

Other times, it is pure nonsense.

Evolution bias also exists within TMs and Move Tutors. Reverse can also happen, where the evolution doesn't get a move of pre-evolution, for example, Icy Wind is obtained by Ralts-line except for Gallade.

The general progress of the things suggest that these nonsensical differences are being reduced. Most recently Doduo got its access to Pluck back, so one can expect that other species will do the same.

Part ii. Species bias:

Another issue that dreads the Pokémon is the species bias. Most of the moves go to the higher successful species, pseudo-legendaries, starters, legendaries and such. Early route Pokémon almost never get large movepools.

This will likely never change, due to the nature of how the game is constructed, and how the more popular Pokémon are marketed.

Part iii. Body shape bias:

This is harder to explain, but generally speaking, most of the moves are either energy blasts, energy beams, or punching moves. This means that supernatural humanoid Pokémon have a larger chance of getting more moves(Tyranitar, Deoxys etc.) while more unconditional body types are doomed to get low movepools(Honedge, Serperior, Swellow etc.)

This will likely change over time, as more moves are introduced for different body and elemental types, but the bias will likely stay, because it is easier to make the said moves than make different wing moves.