Civ V is the first Civ I've ever played, but here are a few things that piss me off about it:
1. The online play isn't all that impressive, the game is just too long to properly play online, unless you can really clear out an entire day for it.
2. You're buying an incomplete game. You get a generous ammount of civs, but only one campaign: one campaign. If you want to buy the others then oops, I guess you have to buy the DLCs. I can live with the Monghols, because they were a free DLC and I understand that the game has to be updated once in a while to work out the kinks, but having to pay for a game you already own? What the hell man?! Speaking of DLCs...
3. The Civs that you have to buy in DLCs are, from what I've heard, way stronger than the standard ones. Korea, Babylon and Polynesia are just so powerful if what I've heard is correct.
4. The diplomacy is horrid. Either I'm doing something very wrong, or the AI sucks so bad that even my allies want to kick my ass no matter what. The game forces you into an agressive playstyle from the very start. I can't be the only one who thinks like this, how many times did you want to stay back and get yourself a nice scientific or cultural victory, only to be forced to halt your progress so you can churn out a huge army to teach that backstabbing Catherine a lesson she won't soon forget?
5. Admittedly this is a pet peeve, but the UN shouldn't trigger an automatic "win the game" voting. A lot of people complain that nukes are overpowered, so why not make the UN a wonder that actually allows you to propose and/or vote on certain international laws, like the banning of nuclear weapons. Like, my suggestion would be something like this: if your resolution gets passed, no other player is allowed to deploy or produce any new nukes (though existing nukes do not need to be dismantled per se). You are free to ignore the resolution, but expect a huge diplomacy hit when you do this (it'd be like China nuking Taiwan into submission, I don't think the international community would ignore such a thing after all the no-nuke treaties). Of course there could be a few other resolutions like... I don't know, but it shouldn't be a trigger for victory! France, the UK, America, Russia and China are currently the permanent members of the U.N. security council, but that doesn't mean all the conflicts in the world are resolved, nor that those five nations rule the world. I'd actually say it's quite the opposite in real life, France and the UK are but shadows of their former glory, and the US is going down that same lane pretty fast.
6. Somehow it feels .... lacking. I don't know what it is.
So in the end it's a fun game, but it could have been better. I expected so much from this franchise, because I've heard it's one of the greatest strategy series ever, but I found myself disappointed. If somebody here wants to correct me, I'd be more than glad to hear what they have to say.