So far, after two playthroughs :
1) City states. I like the concept and most ideas around them, but they should play a more subtle role. There are just too many of them, especially in the early game. Because of their sheer number, there is really no popularity contest between civilizations. I think in the early game, there should be 1 CS per civ, with more appearing gradually as the game progresses.
2) UI issues. I like the new UI philosophy but there are informations that are just not there at all (like luxury resources, which are impossible to track). Fortunately, most of these UI quibbles have already been solved by mods, but it's still strange that such a fundamental information is lacking, while there is just no purpose in hiding them (contrary to the opaque diplomacy, which is probably an intended, though debatable, feature)
Nothing fundamental so far, then, my limited experience with Civ V has been a happy one.
If the AI is as dumb as people claim, it certainly should replace my n°2, but since I don't play at high difficulty levels yet, I don't feel qualified to comment on the AI.