In general when looking at the system,...
* Boring Monster Design: quite possibly the worst of the WotC Era
* Hit Point Bloat
* Game balance between Short Rest and Long Rest classes is dependent on GM pacing
* Action Economy: Bonus Action often feels like a design crutch that incidentally screwed over a variety of different options that are tied to it, such as two-weapon fighting. And IME the interaction between the Attack Action and other actions is often confusing for new players.
* IME, for a variety of reasons, play tends to breakdown at around level 6-8
* Inspiration: IME, it feels like WotC did not even apply half-effort when designing this mechanic, which often fails to engage those who like Fate-like meta mechanics while also irritating those who dislike Fate-like meta mechanics, while also feeling disassociated from the character (even more than it is in Fate). Sure, there are ardent defenders of Inspiration - not interested in how they use it - because, overall, Inspiration feels like it's mostly regarded as a dud design.
* Skills: kinda boring and uninteresting. Maybe would have preferred just ability checks without the skills. Players, IME, tend towards one of the problems of d20 D&D where they engage the skill rather than the action in the fiction (e.g., "I would like to roll Perception."). While this is something that a DM can "correct" through framing, the system tends to reinforce and encourage player engagement with skills.
* Saves: Still leaning too heavily on reskinned Fortitude, Reflex, and Will saves, which leaves Strength, Intellect, and Charisma saves lacking.
* Character Build Choice: Great if you want a basic build and locked into your choice, but not exactly a tremendous amount of choice unless one opts for multiclassing characters. IMO, part the attractiveness for MCing for players is in how it empowers player choice more than pure-classing does. Unless you pick a mage (and even then there is sometimes the illusion of choice and trap options), your choices amount to mostly race, class, subclass, which means that typically your build choices end at around level 3.
* Advantage/Disadvantage: an elegant design, but its ubiquity kinda dulls the game and now comes across as uninspiring with each new addition of how characters can gain advantage
* Expertise: It seems a bit extreme in how it scales. It's one of the few ways that players can improve their skills, which leads to people complaining that rogues and bards can do use "their skills" better than they can, which leads to people trying to find ways to gain Expertise. There could have been better ways to implement the design intent of Expertise without some of its problems.
* Less modular than the initial sales pitch. Sure, there are a lot of dials and knobs, but that was also true of every edition.