The BIGGEST single flaw in 5e's engine, and it is a core flaw that cannot simply be fixed with an optional rule, is the stupidity of saves vs attack rolls. EVERY SINGLE TIME we play 5e and someone casts a spell we now have to go look the damned thing up and figure out which rules it uses. This is dumb, bad game design, and just adds nothing to 5e. It was clearly added to the game as a "well, it existed in AD&D so we sorta gotta emulate what was there", which doesn't impress me in the least. This is why my own game play, which is pretty divergent from stock 4e, is still essentially based on 4e and is not a variant of 5e.
The other problem is defenses. The 5e version of defenses, IMHO, is a bad implementation. I'm not sure why they did it, except maybe to get rid of a 3e/4e ism (the three 'combo' defenses/saves). It makes no sense. It is hair-splitting to say if an attack should target WIS or CHA, WILL would have worked fine there. Also you can at least have a go at an "I have even defenses" or "I have a monster WILL but little FORT" as a choice, but with 6 numbers, you just have to be stuck with where they fall, so you have kind of lost a bit of characterization territory. I don't see what was gained with this change either.
The awkwardness with armor class is not so great either, but then I'm not convinced AC was a great success of the 4e engine either. The whole mess with Barbarians and whatnot and light armor patch feats and such was a mess. The theory was OK, but it didn't hold up well. Still, 5e definitely didn't make the situation better, it just moved things back in the direction of AD&D, kinda, but really all it did was restate armor basic bonuses as a flat number instead of an offset from the base of 10. And yeah, medium armors kinda suck, although there are a few niches where you might want to use them (IE if you have a DEX between 12 and 15 and don't want to wear heavy armor).
In other ways I think 5e did OK, cutting the game to 20 levels of play was good. I'm OK with the range of bonuses and such. It isn't some amazing solution to anything as it is sometimes advertised, but for a 20 level game it kinda works. I don't think it ends up BETTER than 4e's approach though. The ditching of A/E/D/U I think was a bad choice as well though, but you COULD hack that back in if you were really determined. It is just that you might as well just use 4e and avoid the problems above to start with...
5e almost did most things OK, but then it fumbled. I don't like their class design much either, but that's a different story.