5th edition does a lot of things right. Curious to hear what peoples' biggest issues are with it.
I'm gonna guess that most people's problems with it are based on it not fitting their specific preferences. Since it was designed to fit the largest player base possible, it's not going to perfectly fit most serious gamers. On the plus side, 5E is very easy to modify since it sits on a solid chassis (unless you hate the chassis, like I did 3E, in which case you're better off with another edition or RPG). None of my issues are seriously game breaking, and many of them I've simply found fixing to be more work than the problem.
1. Equipment - most expensive armor is always best, medium armor is iffy, weapons are all over the place, a magic item is listed as adventuring gear (potion of healing), and a single piece of adventuring gear defeats the purpose of a cantrip and skill (Healer's Kit).
2. ASI and Feats - fortunately feats are an optional rule, but in any game that uses both rolled ability scores (as many, many groups prefer) and feats (which a lot of groups do), you have an imbalance. Even though the maximum is 20 (and I REALLY wish they'd have kept it to 18), if a player has just better rolls, they will always stay ahead of a worse rolled character, because they'll switch to feats once they max out. Without feats, you instead have a set of diminishing returns, where the better rolled character stays ahead, but in secondary and even tertiary ability scores that matter less.
3. Saving Throws - I love the fact that all six ability scores can be used for saving throws, but the legacy of keeping Dex, Con, and Wis as the primary saves was a hugely wasted opportunity. If the saving throws were evened out, then having a "dump stat" would always be an actual negative. As it stands, most characters can put their lowest ability into Int with little to no consequence, with Str and Cha occasionally following suite.