Charles' hilariously bad "groovy 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.
Amy: First you proposition a girl, and then you call her deformed. How is that seduction technique working for you?
When he's flirting with Amy, Raven irritably joins him at the bar to say "I guess I'm ordering my own drink then." She then uses her powers to give herself two different coloured eyes.
It turns out that Raven isn't all that interested in the nitty-gritty details of genetics:
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.
After making him witness Emma and Riptide's powers, Shaw sends the Colonel back to the latter's headquarters... by summoning Azazel, as if the guy hadn't seen enough that evening. The cherry on the cake is Azazel trying to be somewhat comforting (never mind that he's a demonic-looking teleporting mutant) by calling the Colonel "Comrade."
After Charles is awarded with a PhD, we have this cute exchange between him and Raven.
Raven: Look at you, a professor now, huh?
Charles: Oh, don't call me that, you don't get to be a professor until you have students. Do say "Let's have a drink" though.
Raven: Let's have a drink.
When Moira greets Xavier, he had just downed a yard of ale to celebrate the successful defense of his doctoral thesis.
Moira: Congratulations, professor. Xavier: Thank you very much. It's much harder than it looks, actually. Moira: No, on your presentation.
When Charles starts in on with Moira and her auburn hair, his delivery is a lot more sloppy and he's obviously much more drunk.
The way Charles convinces the Man in Black to come with them.
Xavier: Would you like to see another magic trick? Man In Black: Yes! 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.
The slightly sheepish look she gives them sells it. She's embarrassed because they caught her not doing something nasty.
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)
Particularly funny because Hank was clearly not told of the plan ahead of time. The look he gives Charles when Charles expresses complete faith in Alex makes it perfectly clear that Hank disagrees spectacularly.
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.
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!
McAvoy recounts to TV host Graham Norton a childhood anecdote when he used to practice his "telepathy" on his family's cat.
"When I was a kid, I used to sit there looking the cat in the eye and just going, 'Move. (performs a Pstandard Psychic Pstance) Move.' And every now and again, after half an hour, it would eventually move. And I'd be like, 'YESSS! I'm a mutant!' [...] When I was a kid, I used to believe I could [mind-]bend your cat."
In this crossover parody between First Class and Casino Royale (2006) (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.
X-Men: First Grade, featuring Charles, Logan and Erik as kids with Emma Frost as their teacher.
How about the hilarious coincidence that the villain has the same name as Anakin Skywalker's original actor?
James McAvoy's description of a fight sequence that he and Michael Fassbender had filmed with a very tall actor sounds really funny, but sadly, XMFC fans may never get to see it because the studio and/or the director are embarrassed by it (the Deleted Scene wasn't featured on the Blu-Ray).
McAvoy: There was actually a scene in X-Men: First Class where we come up against somebody so dumb that I can't mind-bend him. We end up having a real deal fight with him, me and Magneto, because there was no metal in the room, either. And we just end up having a fight with this guy who was 7' 6" or something like that, it was hilarious. We kill him by shoving a bear's head over his head. It was weird. [...] we twisted it and broke his neck, and I said something like, "I couldn't bear that man." (laughs) It was a proper sort of ridiculous and fun as hell, but it was obviously silly and we cut it from the film.