According to Paul Haggis, screenwriter on the next James Bond movie (for now known only as "Bond 22"), the next film "picks up 2 minutes after the last one."
If you recall, Casino Royale ended with Bond fully becoming 007 (for lack of a better phrase) with the movie fading to black while finally playing the familiar theme at the very end of the film. I thought Casino Royale was excellent and was just what the franchise needed to rejuvenate it (much like what I'm hoping J.J. Abrams will be doing with the upcoming Star Trek movie).
I'm a bit torn regarding the next film picking up right after the end of the previous one, though. On the one hand it's a cool idea watching 007 on his next adventure right after he fully comes into his own. But on the other hand, I kind of wanted to see Daniel Craig portraying Bond as a more seasoned 007... say, a couple of years later so we could see what a full-on Craig-Bond would be like as a comparison to other actors who've portrayed the character.
I consider Casino Royale to be the Batman Begins of the Bond franchise: A journey of self-discovery showing the man growing into the well-known character he will become. Because I still think that Craig is the closest thing to early Sean Connery as Bond, I'd love to see him portray the character in full-on, "Bond... James Bond" mode.
Oh, and Haggis did reiterate that although "Bond 22" will be grounded in reality, that this one would be "fun." I don't mind a sly bit of humor here and there, but if they go too far I think it's a bad idea.