1. Skills - already vestigial in 5e, I don't really use them, I just add Profiency to whatever ability checks a character should be proficient in by reason of his Class.
2. Multiclassing - this is the bit of 5e that seems most 3e-like. Fortunately it's listed as an optional rule. Disallowed.
3. Saving throws - 5e has this weird thing where most saves never improve, in fact they get harder to make as DCs go up with level. I give every PC Proficiency in all saves, this gives more of a pre-3e feel. I found this doesn't work for monsters though, 5e casters are already much more limited than in other editions and they need to be able to have spells work most of the time or they will seem very weak.
4. Feats - for my Dragonsfoot game I didn't allow them at chargen. I'm a bit torn on this one, but a lot of 5e feats resemble stuff like the Mentzer Classic D&D 'Fighter Smash' attack - stuff that I think is ok at higher level. Again Feats are labelled as Optional and for some groups it may be safer to disallow them if you don't want a whiff of 3e style minmaxing.
5. Death Saves and "heal from zero" - a 4e-ism which is ok-ish in that game, terrible (IMO) in 5e. I don't use them, instead I use negative hit points and when a PC goes deep into negative they'll have trouble getting back up again.