The problem is you cannot finish MP games in a timely fashion unless you play with a severely restricted subset of the whole game (for example starting in the modern era): The game just takes too long. The only alternative to that is to play with people you know, either in real life or over the net, on a regular level.
If I had four or five friends who enjoy playing Civ5 and are of a similar skill level instead of maybe one whose computer can't handle it, one who is worse than the others and one who has no time, I might try playing MP
Then again, I like to play boardgames when I play MP, because you can finish a large number of games in three hours, without one of your friends having to sit around twiddling their thumbs for half of the game because they were defeated in war.
I enjoy CiV. A lot. Even an avid fanboi like myself has found some seriously frustrating issues.
I am one of those players that has 4-5 friends who played CIV BtS constantly in MP and migrated to CiV upon release. We generally run nightly games of 3-4 hour sessions and we load a different game depending on who is up for playing that night. Should someone get eliminated, we put that game on hold until the eliminated player is unable to play. This worked well in CIV BtS, but is causing some issues in CiV due to the poor save/load options or the fact that it's pretty much nonexistant. We're having to migrate save files after a session to preserve them so that the autosave doesn't overwrite the file as we create a new game based on a new combination of players.
Imbalance is an issue but it's not one that is as glaringly obvious as the save/load fiasco I mentioned. Greeks are ridiculously OP when compared to most other Civ choices, Babylonians will be also once/if they get enabled for MP. Great scientists are OP compared to all other Great people, etc... These things are normal in my opinion however and will be fixed as time goes on and the community feedback helps steer Firaxis to where it should be. That or our modding community will correct it.
I feel that the system requirements should have been higher, the game should have been tested on a ton more PC configs, and that it was rushed which shouldn't suprise anyone who has been following the non-Blizzard game industry of late. Again though, these areas are being addressed and hopefully each patch will bring it closer to perfection.
I don't really play single player often, haven't even finished a game yet in SP, but I do notice HUGE differences in the way the AI contacts you and such between SP and MP. I don't think the AI EVER contacts me in MP except to tell me there will be war. No pacts of secrecy, no warnings to not settle somewhere, nothing, nada, zilch.
Where are my animated leaderheads in MP? I can understand and sympathize with both sides on animated combat but leaderheads? C'mon now....
I'm in a rant

Let me stop for now. CiV is great, Harry Potter sucks monkey testicles through a rusty crack pipe, D&D 3.5 for teh win, and hopefully one day, CiV Complete will flesh out the game and make it a worthy ADDITION to the series.