This isn't even a complete list...
Big Things
Lame monsters. Often monsters have no roles. If you attack a gnoll camp, the gnolls blocking the passage to the cave are statistically identical to the ones a few feet behind shooting you with shortbows. Lame monsters have few abilities. Only "leaders" get to be cool.
Unbalanced monsters. Certain classes of monsters (eg ghouls) shouldn't be far more powerful than other monsters of the same "level" or XP value. Monsters can easily be underpowered too, often for reasons of the "flat math", or have really weak saving throws in some categories due to the stat save issue, a problem with 3rd Edition that we don't need to copy again.
Human ability score boosts. This just doesn't make sense to me.
Feats for stats.
Lack of class roles. I don't see why archers should be using the fighter class and getting all the benefits and weaknesses; some of the benefits (eg heavy armor) they can't even use. It's only tradition or the name "fighter" that imposes this. The cleric class is (again) a mess. You tank, you curse, you heal... you're three classes in one (but only one action a turn).
PC casters start with very few spells and end with a lot. It's really hard to balance a system where, once again, wizard power goes from weak to very strong. (And not even all that weak, considering they can get at-will spells.)
Healing is a red button issue. There's a vast gulf between people who like easy healing with hard encounters (such as myself) and those who like logistical depletion. Even a modular game is going to have a really hard time containing both playstyles.
Bounded accuracy was a worthy goal, but the system isn't built to support it. Even things like Dex to AC (which scales) compared to PCs with heavy armor (no scaling) don't work. Monsters can't hit high level rogues but can slap around fighters, clerics, and wizards. Because things like AC aren't predictable anymore, balancing monsters is made far harder. Save DCs scale, but monster saves are based on ability scores.
There's a general lack of spell balance. I'm not pleased that combat and non-combat spells are competing (there's a ritual system, but that's just a name, and nothing like 4e's system). This is almost a red button like healing, as many people want this competition. There's probably no way to satisfy both camps.
I already have 4e. Frankly 4e is already bloated. I shouldn't say I'm happy 4e development is done, but in a way I am glad.
Little Things
Rangers still cast spells last time I checked. Then again, the ranger hasn't made sense from day one and probably never will.
Weird wildshape rules. I think your original stats should play a role, and don't see any need for "extra" hit points.
Kender in the core books. Ugh.
Multiattacks (eg a 5th-level barbarian now gets multiple attacks). It's better than iterative attacks, but I think a single more powerful attack would be faster.
Maybe this should go under big things, but magic items... I don't want them to be required so everyone needs their Big Six or Big Three (3e, or 4e without inherent bonuses), but I don't want a system where there's no guidance to how many items a PC should have and how powerful they should be (2e and earlier). There's probably no good way of resolving this issue. However, +2 and "better" weapons are rare, so it's not a Christmas Tree-sized problem.
Good Things
Backgrounds. Even with the changes, I really like their non-numerical benefits. Soldiers having a rank that contributes to the interaction pillar? Me want moar!
Advantage is something I like. It's probably overused, but I like it. I'm even using it (for a very few things though) in 4e.
Being able to (sometimes) separate ability scores from the specific skills. There might be a time when you make a Charisma + Arcana or Strength + Intimidate check.
