There are basically only two problems with 5E:
1) Everyone's already said it, but Hit Points. Not only do characters have too many HP at any but the lowest levels, but they recover those HP far too quickly, which trivializes any combat that doesn't end in death. It doesn't matter if you get shot for 75 damage, when you can spend nothing and be back to full like it never even happened; and if it doesn't matter, then why are we wasting time on it?
2) Bounded Accuracy describes a bizarre, non-sensical world, where the world's strongest human routinely fails to lift an objects that can be lifted by the world's weakest human. The differences between individual capability are much smaller than the uncertainty of the die roll, which is so far out of line with our daily experiences that it sticks out like a sore thumb.
1. I would like th 4E version of healing surges. something like 3-4 healing for 25% of your HPs during short rest. They would recover during long rest.
2. Bounded accuracy is not the problem, it one of the better things in 5E. main problem of d20 system is the d20. It's too enreliable. 3d6 with bounded accuracy is great. with 3d6 a weak individual with 8 str has a check spread of 2-17 while a individual with 20 str has 8-23 and with a bell curve there is much smaller chance of a weak character defeating strong.
additional.
There should be more 1-2 expertise per class at 1st level.
Especially in a skill that should define a class.
I.E.
Barbarian: expertise in one skill out of athletics, perception, survival,
Bard: expertise in perform, one music instrument, and one of arcana, religion or nature.
Cleric: expertise in religion,
Druid: experise in nature,
Fighter/monk: expertise in athletics or acrobatics,
Ranger; expertise in survival and one of nature or perception
Rogue; expertise in thief tools and 3 skills
Sorcerer: expertise in a skill determined by bloodline
Warlock; expertise in one of arcana, religion or nature. depending on patron
Wizard; expertise in arcana and alchemy tools