Charles' hilariously bad "mutations" pickup line, particularly the second time around. Even funnier is that when he hits on Amy, it appears to be working! What makes it even more comical is that it's basically the same speech (with Xavier narrating) that opens the first X-Men movie, so it's essentially a Patrick Stewart Speech being used to flirt with chicks.
Early in the film:
Raven: I'm sleepy, will you read to me? Charles: I can't. I have my thesis coming up, I have to study. Raven: Fine, read that, your thesis always sends me right off.
When Moira finds Xavier drinking a yard of ale after he had just read his thesis on mutations.
Moira: Congratulations, professor. Xavier: Thank you very much. It's much harder than it looks, actually. Moira: No, on your presentation.
When Charles convinces the Man in Black to come with them.
Charles Xavier: Would you like to see another magic trick? Man In Black: Yes! Charles Xavier: (Using powers, gives order) Get in the car. Man In Black: Good idea.
Emma Frost uses her powers to make an illusion of herself for a Russian general to have sex with while they are "negotiating." Charles and Erik burst in and see the general making love to thin air, and the two of them share a prolonged, silent "WTF?" reaction.
Shaw invades the CIA building to talk to the mutants Xavier has gathered, and asks Azazel if the other telepath is around—he says he isn't, and Shaw says, relieved, that at least he can take the silly-looking helmet off.
Havok and Banshee get a few during the training montage, with the former making Charles rush for the fire extinguisher in a panic and getting knocked over by his power, and the latter failing to fly from a window and landing in the hedge, and then getting pushed (by Erik) off the top of a satellite dish.
Doubly hilarious is the conversation just before he's pushed.
Banshee: (to Xavier) I trust you! Xavier: I'm touched. Banshee: (about Hank) I don't trust him. Xavier: (to Hank) Say nothing. Banshee: I'M GOING TO DIE! Xavier: All right, look. We're not going to make you do anything you aren't comfort— Erik: Here, let me help. (shove) Banshee: AAAAAHHH!
This bit afterwards:
Xavier: Erik! Erik: What? You know you were thinking the same.
And then later this scene comes back in an amusing way when Banshee is about to drop out of the Blackbird to locate Shaw's submarine, where he notices Erik is coming up behind him to the open bay doors. Clearly, getting pushed from a great height once by Erik was enough.
Banshee: Whoa! You back right off! (Erik knowingly smirks and raises hands apologetically)
When Erik convinces Raven to stick to her true blue form, she goes down to talk to Charles with no outer clothing, which startles him. Although she takes this to re-affirm that she's done hiding her true self, Charles's awkwardness is more from the fact she's technically stark naked and he considers them Like Brother and Sister.
Charles: Yah! For God's sake, Raven! Where are your clothes? Put, put, put some clothes on!
And from the deleted scenes, the infamous Dragneto, plus Xavier's line immediately afterwards.
A Real Life example: When James McAvoy learned he got the role of Charles Xavier, he shaved his head without telling the producers because everyone knows Professor X is bald. Turned out that they needed him to keep his hair because Charles still has it in the era that the film takes place, which resulted in McAvoy having to wear hair extensions throughout filming. Whoops!
In this crossover parody between First Class and Casino Royale (which is appropriate because XMFC was inspired by '60s-era James Bond films), Erik Lehnsherr is 007, Moira MacTaggert is M, Sebastian Shaw is Le Chiffre, and Charles Xavier is... well, let's just say that the character he embodies also has access to money and harbours a strong aversion towards violence.