Let's be honest: it absolutely does not matter how Spider-Man got his super-strength. Audiences are just as likely to believe that a man can lift a car over his head as they are to believe that being bitten by an irradiated spider can give you "spider-powers" (whatever those are) so why have there have been two separate movies that spent an hour of their run time trying to explain something that doesn't need explaining with an explanation that doesn't make sense? Why not just cut to the chase and show us a guy being super strong?
Or to pick another example: the first Hulk movie went into depth showing us how he gained his powers after he was dosed with gamma radiation, but that movie was so unpopular that I have to imagine that a large percentage of the Avengers' audience had never seen it. Were they confused when Bruce Banner got bigger and started punching stuff? Probably not. If they hadn't absorbed his backstory via osmosis before the movie came out they probably picked it up from the context of the film; the rules that govern what he can and cannot do aren't complicated.
It shouldn't be a biog deal that X-Men First Class is a good origin story movie, but it is kind of a big deal, because comic book movies have been so consistent about getting that wrong. Unlike other franchise-starting films, the first hour here isn't wasted: mutants show up and start mutant-ing pretty early. There is a lot of exposition in the film, but the flashbacks it shows us are meant to explain people's personalities or to set up relationships that are necessary to move the story forward. Focusing on character instead of gibberish about radiation is a smart move.
And yes, I understand that a big reason why the film doesn't fall into the typical origin story trap is that the X-men are mutants, and the whole "mutants are just born with powers" thing makes in depth back stories unnecessary. And yes, I understand that the most likely reason why they cut all that stuff out is that they have to introduce too many people to be able to give all of them personal histories. We start off by meeting the people that will create Professor X's school, then we meet the first team of mutants he's training, and then we meet the rival team of mutants they have to fight. At a certain point with that many characters you have no choice but to say "yeah, that guy who looks like the devil has the ability to teleport, let's just accept it and move on." So the fact that it doesn't overkill us with exposition doesn't mean that it isn't overstuffed in other ways.
In fact, the film's biggest weakness is it's overabundance of characters. Sebastian Shaw, the main villain, wants to play the Russians against the Americans in an homage to the Cuban Missile Crisis, which means that in addition to having to meet so many mutants you have to meet a lot of humans who are involved in a fairly intricate plot. For the most part the story remains coherent, but there are times when it starts to drag because there's too many balls being juggled at the same time. When it all comes together at the end it feels satisfying, but it is a lot of work to get there.
The question, then, is whether X-Men First Class' flaws overpower it's strengths. Is my annoyance at the sheer amount of plot this movie crams in enough to overwhelm my gratitude at seeing an origin story that doesn't try to bullshit me with unbelievable pseudo-science about magical radiation? It's a little hard to say. Whereas those other movies start badly and then build towards being more interesting, X-Men First Class alternates being frustrating with being good. (Oh, they did a great job of casting - that actor is great in this role. Wait, where did they go? I haven't seen them in 20 minutes because there are so many people in this movie!)
Oh, who am I kidding. I'm the sort of nerd who nitpicks these movies but keeps on watching them anyway; I'll keep watching them even if I don't expect to enjoy them, so even small bits of pleasure are a plus. I might not love the fact that I like this movie, but there's no point in denying that I do like it, flaws and all.