WARNING: SPOILERS AHEAD!!!
I think the whole movie is darkly funny. John Malkovich's character having graduated from Ivy league and refusing to admit to himself that he's just not that important. When he starts recording his memoirs like they're something anybody could ever possibly give a ---Cleveland steamer--- about . . . and his stupid, pompous, self-important voice and manerisms while he did it. Francis McDormand's motivation through the whole movie, even after all of her friends were killed thanks to her. The misplaced sympathy you had for George Clooney's wife, only to find that she was cheating on him all along and about to leave him for her lover. That both Clooney's wife and his lover deluded themselves into thinking that they were pleasant while the other was a cold ---smurf---.
I didn't think George Clooney's invention was especially funny. It was Francis McDormand's reaction to it that was ---smurfing--- hilarious.
And the CIA director . . . ---smurfing--- hilarious. His raison d'etre was to avoid having to do anything. Not just himself, but the entire agency. Do everything possible to be able to do nothing.
So much more. I think it's a very detail oriented movie that could easily be ruined by the company with whom you watch the movie, or the mood you are in when you watch it. A lot of the comedy and insight is in small details, easy to miss. Worth another watch if you liked it, cos you'll likely grow to love it. If you can bring yourself to it, it's probably worth another watch if you didn't like it, but I'm not really sure I'm THAT persuasive.
edit: pronoun trouble