Most people seem to complain about the most silly things in this thread.
The game is pretty good, the diplomacy needs some work but they are fixing that in the expansion so it's all cool.
Also Eurocentrism? What do you want then? South-Americacentrism?
Thing is, the European countries are the norm, America started as nothing but colonies from European countries and pretty much all non-European countries and civilizations died out early or were technologically behind.
The only exceptions being some countries in Asia which had the same technologies but were a bit ahead.
Lets see the actual problems of the game, listed in order of importance:
1) 1UPT breaks every other aspect of the game. They had to drastically slow down production, and population growth in order to ensure that Carpets of Doom didn't appear in the BCs. For a game which is based not around war but around building a strong empire, this was a horrible design decision.
2) The AI is both stupid
and insane. The AI civs do not know how to use their units or advantages. In the game I posted earlier in the thread (or the US based counterpart) someone said (in paraphrase) "I'm worried about Ghengiz's keshiks, except the AI has no clue how to use them." If the AI cannot use the war mechanics, why implement them that they are now the dominant part of the game? The AI has been likened to Monty from Civ 4 quite a lot, though from what I've seen I'd go farther and say they've gone back to Civ 3 levels of insanity, where chance of a war dec is just a dice roll away. You can't stay friends with the AI, they'll just get angry over something they did. You can't help the AI, they'll just hate you for helping them. You can't join a dogpile you've been invited to, they'll call you a warmonger and try to backstab.
3) Most of the diplomacy exploits from Civ 3 are back, but now with the addition of city states you can break the game harder and more easily. You can sell luxuries for huge sums of gold, and then pillage the resource to break the deal, turn around and ally with a CS get a new resource, sell the two resources, for even more money, and repeat from step two. And they invented some new ones, like great scientists bulbing every tech in one go. Frankly this game was never tested in the first place, and quite a few of the more egregious exploits have never been removed.
4) Civs are massively imbalanced, way more than in any version of Civ 4. Some traits or UUs allow you to conquer the world at ease, while others are just sad (though that doesn't stop you from conquering with ease). Another sign of the absense of testing.
5) The game was (and probably still is from what I can see) way too easy. Deity was broken within a couple of weeks of release (by Sullla and co., RBSG3), while using the then weakes civ. People will say that the game was beaten by a group of top level players. Well there's two problems here; 1) The mechanics changed so much that previous experience should have counted for little, and 2) I don't think a single one of those players managed to beat deity for a long time with base Civ 4 (BtS Deity is by all accounts somewhat toned down), if at all. So playing the same level of an unfamiliar game, that they could only occasionally beat on a game they're pretty much experts on, means pretty much that the game was a pushover.
Pretty much everything else is lesser than this, but each single one of these five problems is a game breaker.
Note: While Firaxis had people on board designated testers, and a process called beta testing, it is obvious that when a game is released to the public in essentially a pre-alpha state, that neither of these things were set up to do what their names meant that they should do.