Favorite:
1. Simple efficiency of the Fighter, Rogue, Cleric, and Wizard; every class feels different, even when it's all just variations on basic attack and spellcasting.
2. Feats as optional.
3. Backgrounds. None of them in particular, but just the idea that your skills come from your background, and you don't really pick up new skills just by wandering around.
Least Favorite:
1. Ability scores, just in general. How the score doesn't mean anything, but the modifier does. How characters have a functional range between 8 and 20, so the weakest mage can beat the strongest warrior in arm-wrestling.
2. The implementation of two-weapon fighting, where everybody in the world can (and should) do it.
3. Fast healing by default, and the difficulty in narrating an attack where no lasting damage is inflicted. The devaluation of magical healing, which can no longer affect anyone beyond what could be accomplished with a long rest.