I haven't seen the CG bug yet, but I'm guessing I will sometime soon.. Here are the problems I have seen however:
1) The biggest problem, which is a serious problem, is that the game desyncs after 5-30 minutes of playing (4-40 days or so ingame would be my guess). This is possibly releated to game performance since it appears to happen more frequently when playing in higher speeds (3+), but it also happens in lower speeds. Perhaps it should be noted that both of us played as Germany and used manual control of everything (the controlled tech and intelligence, I controlled production and most diplomatic actions).
2) Also, try loading a game in the multiplayer screen (the screen where you select which country to play), then have someone join your game. For me and a friend this had the effect of resetting my date to 1 jan 36, while he got the right date. The game desynced the second it started, but I could continue. While the date was wrong, the game was loaded, so I was back in 36 with all my techs, installments and produced stuff.
3) When two (or more?) players play as the same country, in my case Germany, only one gets events/decisions and those round alerts/messages/whatever in the top of the screen. This makes alot of sense really, but it would be great if the host/first player could select who should recieve them, or if everyone could recieve them but only one make the decisions or something.
4) Possibly releated to multiplayer somehow, sliders (production and leadership) tend to jump back to where they were if you make a change and don't save (close the dialog) immediately. VERY annoying. This is not the same as (5) as we don't use the same interfaces at the same time when this happens.
5) Also on sliders in multiplayer, as changes are saved/updated on close, two people cannot access the same interface at the same time while playing as the same country. For example, if both me and him open the technology screen, he makes a change and exit, then I exit, his changes will be lost I think. Either that, or if he makes a change, then I exit, his changes will revert before his eyes. At the moment we simply don't use the same screens at the same time, which sucks since we can't agree on which techs to research or units to produce and so on.
Perhaps (4) happens when someone closes an interface, even if it's not the same. Are the production sliders saved (sent over network) when the technology window is closed?
(Also annoying is the wasted IC warning which is completely useless at the moment. I don't want to use the AI sliders, I want to manage these myself, and I really don't care if I waste 0.02 IC on supplies)