How in the world can Charles possibly convince his parents to adopt a strange, little girl who broke into their house... oh right, he's a telepath who can control minds.
Xavier ensures that Raven only drinks cola when they hang out at the pub because he doesn't want to risk her becoming intoxicated, which could affect her concentration in maintaining a human form in public.
Why is Charles is so overprotective of Raven? It's because he grew up resenting his mother's Parental Neglect, and he made a conscious decision even as a child that he'd never be like her. Of course, he doesn't understand yet that suffocating someone with love is also bad in a different way, no matter how good one's intentions are.
Raven's near-instant attraction towards Hank is very natural when you realize that he's essentially a younger, more introverted version of Charles. She's subconsciously transferring her quasi-romantic feelings towards her brother figure to a similar, dorky guy who is much more accessible to Raven as a potential boyfriend. Bonus points for casting Nicholas Hoult, who is pretty like James McAvoy (both actors are boyish-looking, brown-haired, blue-eyed, with reddish lips and a pale complexion), which would make Raven switch to her new object of affection that much more quickly.
Why would Shaw kill Darwin despite the whole "protect our own" thing? He's a Nazi. He might not be interested in focusing his hate on Jewish people, but the Jews weren't the only people they were racist against. Moreover, he already stated it clear how he and his crew would treat those who oppose joining him no matter what breed they represent.
Sebastian Shaw: Be enslaved or rise up to rule. Choose freely, but know that if you are not with us, then by definition, you are against us.
You would think Erik would get chewed out for endangering Banshee by throwing him off a friggen satellite dish. Except he could always pull him back up by the metal in his clothes if the training fails.
When Charles teaches Erik that his powers are strongest "between rage and serenity," he's saying he has to master both positive and negative emotions. True magnetism right there.
At the climax when Xavier begs Magneto to spare the soldiers that fired upon them, stating that "they were only following orders," that was indeed one of the worst things to say to a Holocaust survivor of all people, but it's brilliant when you remember that Charles was a telepath for the majority of his life and could always look into people's minds to say the right things to get them to do what he wanted. The only person he refused to scan was Raven, and he therefore often made insensitive comments around her. With Magneto wearing the protective helmet, Xavier has been deprived of a sense that for him is as vital as sight, so when he unexpectedly loses it, he found himself in the position of a man who is suddenly blinded and is required to process visual cues.
Although "La Vie en Rose" serves as Shaw's Leitmotif, the title (which can be roughly translated as "Life Through Rose-Tinted Glasses") is actually an apt description of how the optimistic Charles perceives the world.
Xavier's cheerfulness mirrors the positive outlook Americans generally carried under President Kennedy's administration. It may or may not be a coincidence, but Charles' personality and background are fairly similar to John F. Kennedy's. They're both Old Money, charismatic, handsome skirt-chasers with leadership abilities, and they were born with a condition that they want to keep secret (Kennedy hid his Addison's disease from the public).
The reason why the barman in the Villa Gesell spoke Mexican Spanish: He was a Nazi spy in Mexico, was found out and fled where the other Nazis and Nazi collaborators fled: Argentinia of course!
Shaw's mutant minions are all extremely powerful mutants in their own right. Why did he have such potent subordinates? Easy: he started almost 20 years before Charles and Erik began searching for new mutants.
A lot of people think Mystique's defection to Magneto was rushed, but take a closer look at events. Every time she shows even hints of her real form, Xavier criticizes her, making her feel less comfortable about herself, leading to her maintaining a human cover, which puts a strain on her. Note than in the first scene with her as an adult, she takes on her mutant form when she's not in public. Following that conversation with Xavier, she maintains a human form all the time, even when she's with her friends, other mutants. Then she finds kinship in Beast, who also does not accept her real form. The only guy who encourages her to take the emotional pressure off of herself and be who she really is, is Magneto. She didn't go to Magneto simply because she was in love with him, she went because she no longer felt comfortable hiding who she was and living a lie due to her brother.
There's potentially another side to this, though. Charles is uncomfortable when she brings up dating him and shows up naked, sure, but has no problem with platonic cuddling when she's dressed. Erik effectively tells her her natural body is a costume, and needs no further covering. As far as acceptance goes, there is room for interpretation. Plus, it's not like she wouldn't have to hide with Mags, too.
There is constant mention of Neanderthals and Cro-Magnons to parallel the rise of mutants, which is a nice call-back to a scene near the beginning of X-Men 2 when Storm explains the history of Neanderthals with modern science hinting that Neanderthals might not have been wiped out completely by Cro-Mognons. Science Marches On indeed!
Take another look at the Cerebro scene, while Charles is tracking down the mutants. The typical humans are shown in black and white, while the mutants are in full, vibrant color. It occurred to me after this film that this is how Charles sees mutants in relation to the rest of the world. Humans are old-fashioned and dull, while mutants are vibrant and beautiful. An indication that for all of his talk of cooperation between humans and mutants, he isn't free of his own prejudices? (wallwalker)
Don't forget that Cerebro is a mutant detection system. What sense is a detection system if it doesn't mark the things you are looking for to make them stand out? The humans are no mutants, therefore not relevant, therefore not marked.
Mystique working those oversized barbells in First Class may have been their explanation for her level of badass in the first three movies, turning from a traditional Femme Fatale into the martial arts expert of the comics and cartoon.
In the comics, Darwin just teleported away from the Hulk rather than adapt into something that could beat him - which helps the fan theory that he survived Shaw's cherry bomb, by teleporting away and leaving the exploding blast where he was.
He could transfer his energy to Havok since he survived like that his very first time as an X-men.
The film is a Deconstruction of the Silver Age, which is appropriately where its origins lay. Charles Xavier, brilliant scientist and cheerful patriot for his country, ends up betrayed by his own country for being a mutant and has his best friend and his adoptive sister leave him when it became apparent their ideals differed from his. Erik Lehnsherr, Holocaust survivor and Anti-Hero, ends up adopting his enemy's philosophy and turning against mankind. The teenage super team ends up with one of their party missing, two performing a FaceHeel Turn, and the other three deeply traumatized from having to fight. Science ends up causing many problems as well as fixing them. The idea of having nuclear power enhance the X-gene is immediately scoffed at. Women and minorities are pushed into the background and therefore either lash out (Mystique and Angel) or prove much deadlier than they appear (Moira and Emma Frost).
In the first three X-Men movies, I always wondered why Mystique was nude besides Rule of Sexy. Even in the the comics, she at least had some type of clothing. In First Class, we get to see her struggle with her appearance and wanting to be normal. Even with her fellow mutants, Raven keeps the appearance of looking like everyone else, hiding her her real appearance. When Erik comes along, he tells her that her true form is beautiful and encourages her to stop trying look like everyone else. In the scene where she appears in her natural blue appearance nude before Charles before the big mission, we not only see how they've grown apart but when she stops hiding her true form. Her being nude shows Raven is no longer hiding her true self and no longer conforming to society.
Charles leaves Shaw paralyzed momentarily, so he can't hurt Erik. Then, Erik proceeds to kill Shaw by driving a metal coin through his head. Erik is now delighted he has killed and tortured his enemy- cause let's face it, a metal coin through the skull will hurt. Wrong. Charles had incapacitated Shaw by putting his conscience into Shaw's head so to control him. It was Shaw who died because it was his brain the coin was put through- but it was Charles who felt every moment of a small, metal, object being driven through his skull. Nice one, Erik.
Since Charles hadn't reached puberty yet when we see him as a kid in 1944, that means a traumatic event triggered his mutation—most probably it was the death of his father.
Erik has plenty of reasons to hate Shaw, but one that I only thought of on a recent rewatch... Shaw killed Erik's mother with a bullet, something that's made out of metal. If Erik's powers were advanced enough, he could have EASILY stopped the bullet, or just stopped the gun from firing at all. Meaning it wasn't just Shaw killing his mother... it was Erik failing to save her TWICE. He couldn't move the coin, and he couldn't stop the bullet either