Contrary to most here it seems, I'd have liked them to strip some things out, simplify others, complexify others, and generally go more gritty-less superhero. Some specifics:
Inspiration - metacurrencies like this just bring the metagame front and centre. Get rid of it, without replacement.
Lucky and similar mechanics that can post-hoc change a roll whose result is already known - get rid of it.
Multiclassing - just encourages optimizers and leads to broken combos. Either get rid of it entirely or make it clearly and obviously suboptimal in all cases.
Slow down the level-advance rate and make training to level be the default, in order to a) force some in-character downtime and b) allow a campaign to last longer if desired.
Add in downtime as a fourth pillar and provide downtime activity guidelines.
There's too many classes as it is; several (Paladin and Warlock for sure, maybe others) could be stripped out without really losing anything.
Notwithstanding the above, there's room for a Swashbuckler class and a Cavalier or Knight class.
Put more emphasis on random elements.
Make resting far less beneficial in all cases, particularly overnight hit point recovery.
All of the above would or could be backward compatible.
What wouldn't be so backward compatible:
Design for levels 1-12 with open-ended design beyond that e.g. each x-levels beyond 12th you gain this benefit, each level beyond 12th you gain this many hit points, and so on (1e sort of did this but it can be done more elegantly).
Abandon the "tier" concept - I've never seen the point - and just have levels be levels.
Abandon the hit-dice concept for healing - I've never seen the point of that either - and just have hit points be hit points when it comes to getting them back.
Use flat bonuses/penalties to rolls where it makes sense and adv-disadv where that makes sense.
Encourage DMs to have check results be on a sliding scale rather than binary pass-fail.
Much stronger niche protection for each class, with harshly limited abilities for any class to impinge on the niche of another.
Adopt a Wound-Vitality or Body-Fatigue hit point system.
Make Rangers more Fighter-like and less Rogue-like.
Get away from the idea of Rogues being primary damage dealers; that should be the Fighters' job.
...and about a hundred other things I can't be arsed to type out right now.