Rant time! (Sorry, but you basically gave me permission). I want to preface this list with one thing- in my opinion, it should not be the DM's job to figure all this stuff out without any real guidance. The game should take these things into account and the DMG should go into great detail about the potential pitfalls and problems. Some D&D editions do this better than others, and might even have multiple DM resources (a DMG2, for example). Others...do not. Very rarely are these things resolved for inexperienced DM's.
Further, despite this, I love D&D. I may like some versions better than others, but fantasy TTRPG's are my jam, and one way or another, I always find myself playing some version of D&D. But you can love something and still be frustrated by it!
1) The Social tier in general. It usually comes down to one of two things:
*Social stats don't matter because everyone just roleplays their characters and can use their natural "persuade the DM check".
*Roleplaying doesn't matter because it comes down to die rolls. Oh sure, the DM might grant a bonus to a roll, but I've given fairly eloquent speeches and rolled natural 1's, and watched half-baked idiots persuade dragons to back down with natural 20's.
The worst part being that both approaches can happen in a single session, lol.
2) Traps. More of the same. Either people "MacGyver" around them, bypass them with spells or magic items, or it's just binary "roll, you found the trap. Roll, you bypass the trap/you fail and take damage". Not very exciting, even if failure equals character demise.
3) Saving throws. Dear God, saving throws. The difference between being able to actually play the game or not comes up to a single die roll that you usually have precious few resources to influence. What saves your character is good at is basically decided for you by game design- if you're a Fighter, it's really hard to have, say, a high Wisdom score, since the game has decided that you're A) probably not good at saving throws that require Wisdom in the first place and B) your class is built to gain more benefits out of Str/Dex/Con (depending on edition). Please, no comments about how "well, with point buy, you can have a 16 Wisdom easily by and still have a reasonable Str/Dex/Con/whatever- the game has always rewarded specialization more than a "Master of None" approach. Having a 14 in every stat isn't going to save you and might (depending on edition) completely hamstring your character.
4) Point-buy. Now obviously, playing character creation like a lottery and having some characters be better than others is problematic. But not every class has the same priority for ability scores. Your 21 point buy Fighter is going to function a lot better than a 21 point buy Monk, and the 21 point buy Wizard might make out like a bandit in comparison. Just build your system to give players the ability scores their character needs to function properly if you know randomness is bad!
5) Magic items. Just...why. When I first got into D&D, magic items were the premium rewards for your character, giving you unique advantages and abilities. From the simple utility of never running out of food with a Murlynd's Spoon to the awesome potential of a Rod of Lordly Might. But the game has never figured out how to actually add them to a game without causing havoc. From random drops, adventures dripping with "must haves", wealth by level, item creation rules, wish lists, limits on how many can be used- it's a huge mess, and every "fix" just makes magic items less special and awesome. And despite having no clue how to balance magic items, books are still printed with gobs and gobs of the darned things! A game without magic items is pretty boring (IMO), but a game with magic items requires the DM to carefully curate what the players can have at every turn "oh I better not put +2 armor in this adventure, the Cleric has too high AC already. Nope, no flying items, then I might as well write off melee monsters forever. A cube of force? At that point, the inmates are running the asylum!
5a) Boring magic items. What the actual...I can't even. A +1 sword? Really? If your game absolutely must have accuracy and damage bonuses, bake them into the character! Tiny numerical bonuses handed out as treasure? "Hey Mr. Fighter, here's your reward for adventuring- the ability to actually fight higher level foes!". Bah! Even worse if your game supposedly doesn't actually need +X swords or armor- why even have them, then?
6) High-level play. If your game stops being balanced like, at all, once characters reach a certain level, just don't have those levels. Or at least, tell DM's "advance at your own risk"! Especially since everyone knows you're going to support the low and mid levels way more with products because it's not cost-viable to make many high level supplements!
7) AC. Why do trained warriors have so few active defenses? Why is so much of the game about hiding behind a number? Why is there a soft cap on that number, when monster accuracy skyrockets at higher levels? Why is AC so high at low levels, when stuff can barely hit? Oh because enemies do too much at low levels and too much at higher levels? FIX THE DAMN DAMAGE VALUES THEN!
8) "Adventuring days". For the love of all that's sacred and pure- NOT EVERY DAY HAS PEOPLE FACING 6-8 FIGHTS (or whatever number your game "assumes"). STOP designing character classes that can be wildly stronger or weaker depending on whether you're exploring a MegaDungeon or just traveling from town A to town B! Not every road can have bandits or monsters tromping around! In fact, most probably shouldn't, otherwise there wouldn't be any trade or society to speak of! Having a system where some guys have to worry about daily resources and others don't, and where you can trade unspent resources for increased power is ludicrous!
9) If your world has magic, take that into account! If I can build a castle and fortify it with a few spell slots, then that should be reflected in the setting! Even one guy who can use magic is going to have a huge impact on society, and then you have settings where you can't throw a rock without hitting a spellcaster that are all in this vaguely "medieval" setting! And if flying chimeras, dragons, manticores, wyverns, vrocks, arrowhawks, harpies, and rocs are all threats to society, why are there so many fortifications that are useless against flying foes all over the place?! Pick a lane! A world probably shouldn't be low and high magic at the same time!
9a) If magic is a thing in your world. If it's as useful as the PHB would have you believe. If anyone can learn magic, as the PHB would have you believe- why doesn't everyone learn magic? Why leave it up to the DM to answer that question? You'd think every blacksmith would learn basic spells like Mending, Make Whole, whatever to help with their craft, and every warrior would be armed with attack cantrips that obsolete ranged weapons!
10) Are the PC's special or aren't they? A classic question, and one the game never answers- are Fighters a dime a dozen? Wizards? Clerics? Are Elves super rare and hardly seen but your party has three and a half of them? Again, pick a lane!
11) High-level NPC's. If I had a dollar for every time some 11th level guy asked my 3rd level guy to take care of some major threat to their community, I'd have a lot of dollars! I'm not saying there shouldn't be a place for low level adventurers (there wouldn't be much of a game regardless), but it's just too suspect when more capable people always have some reason not to handle threats themselves! Maybe not have all these high level guys around? Just a thought.
12) Downtime. I touched on this briefly above, but sometimes the game doesn't revolve around monster fighting. Sometimes the players have a week or two to spend in town. So why is it that some characters have a lot more to do than others? Wizards could scribe spells, scrolls, brew potions, make magic items, engage in research, or just cast Legend Lore every day to learn about future objectives. Fighters...go looking for an underground street fight? One of these things is not like the other!
Ok, whew. Winding down a bit. There's more, but these are some of the major sticking points, again, IMO.