really need to write this answer once so I can just link it or copy-paste it.

The core dice mechanic is kind of bad. 1d20+stuff gives you flat probability. Every outcome on the die is equally likely. So when you try to throw a dart at the dartboard, you are just as likely to get the best possible result as the worst. That's not really have life works. Compare a dice pool where you are more likely to get a result in the middle.

Combine this big, flat, random factor with bounded accuracy and the limited ways you can get bonuses, you get fighters at +0 outperforming wizards +5 at arcana more than you'd think.

D&D tends to be binary pass/fail. If the DC is 15, typically you get the same results when you roll a 15 as a 25, and the same failure if you roll a 3 as a 13. This is limiting and kind of weird. There are a few exceptions (eg: sprite poison), but mostly this is how it works. I think PF2e has degrees based on how much you hit or missed by. Fate has "Succeed with Style" when you beat the target by 3 or more. Unknown Armies has "cherries" on certain rolls. Lots of cool stuff you can do that D&D just doesn't.

D&D doesn't really have a succeed-at-a-cost mechanic codified. There are countless threads where new DMs are like "My players failed to pick a lock and now I don't know what to do." Putting aside the "don't make them roll if failure isn't an option" advice, other systems solve this by letting players succeed at a cost. In D&D a DM can adhoc do this, but it's not codified. You never know what you're going to get with a new table, and you probably have to explain why this is a good idea from scratch to every new DM. And they might just say no. The rule just isn't there. Compare Fate where you can spend a fate point or succeed at a narrative cost, or even CofD where you can spend willpower. D&D kind of has a baby version of this with Inspiration, but it is extremely under baked. Most tables don't really use it.

The way AC and HP work are kind of weird. Your fighter in armor with a shield is just as hard to "hit" as your nimble assassin in a robe. But when the hit does land, the damage range is the same for both. Since you gain HP as you level automatically, you can't really build a "hard to hit but goes down when something connects" very well like you could in other systems. Nor can you really build a "easy to hit, but hard to hurt".

The mapping between attribute and bonus is a completely unneeded step. Why is 15 strength +2? No good reason. They should rip out the middle step and just say "You have +2 strength."

There are very few choices to make when building your character. You have your class and subclass, but beyond that there are very few viable choices. You probably want the stat up at 4, but you may choose a feat. Most games don't make it to 8, but you have the same problem there. Some subclasses have a couple choices, but usually they're limited to a small handful every couple levels. Bear barbarian vs wolf. Some levels have zero choices at all to make. It is very hard to make a character that mechanically is interesting, distinct, and performant.

There's not a good way to defend someone else. You can take the Protection fighting style, if it's available, but that's a pretty big opportunity cost for the style and using your reaction. The dramatic "dive in front of them to take the shot" just isn't representable in D&D. Contrast Fate where you can always roll to defend someone else if the group agrees it makes sense.

The entire game's rhythm is designed around the "Adventuring day." That is, ~6 medium encounters per long rest, or ~3 hard encounters. The idea is that the long-rest classes (wizards, paladins, bards, etc) will slowly run out of resources throughout the day. It's expected you get ~2 short rests so your short rest classes (warlock, fighter, etc) can blow their whole load more often. But this has several problems. Primarily, it's that most people don't play this way. Apparently most groups do like one big fight per rest. If you do that, your long rest classes are likely to extremely over perform. They'll spend five fights worth of resources in one fight. Meanwhile, the short rest classes can't do that, and will feel weaker.

There are endless posts where people try to fix this problem. "Gritty realism" and "sanctuary resting" are the most common solutions. Personally I think that's a dirty bandaid on the more fundamental problem, and the game should just shift to per-encounter powers like most people already play anyway. Most people don't actually want to play fantasy vietnam where they have to manage their resources wisely. But that's sort of what D&D is built around.

The magic system is kind of bad. Every spell is bespoke and there's no clear way to reason about the system or create your own effects. What level is a spell that paralyzes a person? What level is flight? What level is a spell that lets you fly and paralyzes anyone you fly over? Who knows. There aren't great rules for this. The DMG has some guidelines, but many of the published spell don't follow it.

Every kind of magic is basically the same. You declare a spell, you tick off the box, and the effect happens. Maybe it has a to-hit chance or the victim has a chance to resist. Go read Unknown Armies for some wild magic flavor. There are so many other ways magic could work. Just off the top of my head:

• Ramp up. Each spell opens up options for bigger, more powerful, spells in the subsequent turns.
• Overheat. Each spell increases the risk of a problem Each of those has many variations within them.

You could also do a lot more with spell customization. Go look at Mage: The Awakening 2e. In that game, when you cast a spell you have a ton of knobs to adjust. You can change the area, subjects, duration, range. You can make those bigger and increase the chance of the spell fizzling, or make them dramatically bigger and risk the spell backfiring.

There's a ton of options for what you could do with magic, but D&D is somehow very bland and crams everything into the same chassis.

The rules for social conflict are barely there. If you encounter a pack of bandits on the road and you decide to fight them, there are a ton of rules for how that works. You roll initiative, you make checks against each other's armor and HP, and you're off to the races. But if you instead want to talk your way out, there's barely anything. It's entirely left to the DM to decide. To some people this is a feature. I doubt those people would say it's a "feature" to leave physical combat largely up to the DM, but here we are. Go read Fate for an example of a system that does social conflict reasonably well.

There are not very many rules for engaging with the environment. Many players have had the creativity crushed out of them when they try to do like "I swing on the chandelier and drop kick the orc!" and the DM makes a call that makes that less fun and less effective. "Uh, roll athletics. Oh, a 9? I guess you fall down lol.". Or games get dragged down when players realize "hijinks" like flipping over tables is more effective, and now every conflict is a bunch of adhoc things. Compare Fate that has this built into the game and codified better.

There's not really a way to map description to mechanics. The DM describes "The bouncer is easily six feet all, muscular, and grim. There's a black club leaning against his stool." You have no way of knowing if that guy has 10 HP or 100. If he makes one attack or four each round. Compare CofD where you can estimate "ok he's muscular so he's probably got 3 strength, and a bouncer is probably adequate at hand-to-hand, so he's probably throwing at least 5 dice in a melee." Or Fate where you can be like "Bouncering is his main thing, but he's not like a Big Deal, so he's probably got like +3 at beast in stuff a bouncer does." In D&D you just have no way of knowing. This also sometimes turns into the world "leveling" with the party, which is weird. The DM wants to keep the PCs in line, so the "city guard" is always a little stronger than them.

But even aside from trying to gauge how strong people are, it does a poor job of that for monsters. You describe a giant spider demon in its den. The players have no way to know if that thing has 50 or 500 hp. Yes, yes, in real life you can't see HP bars, but you get a lot more information in real life.

Even if you accept the conceit of hp and levels are kind of unknowable for the player, D&D 5e provides poor tools for creating encounters. People routinely complain that making balanced encounters is hard, and the recommendations from CR don't really work. Part of this is because the long-rest adventuring day concept sucks, and unless the fight is hugely overtuned, the only hard fight of the day is the last one. The earlier ones you can burn more resources to avoid a loss.

Ok. I think I'm done. Maybe I'll save this one to paste later. Ask me whatever. I could go on all day about why D&D isn't as good as it is popular.