I'm not really an X-Men fan but I did find the film enjoyable.
Things that did not make sense to me:
1) Why did Xavier mind wipe Moira? Did he think she would betray him in some way? What was the point. All that did was effectively discredit her for her superiors.
2) Why exactly did the US and Russians suddenly get all buddy buddy and decide to kill the mutants on the beach? That actually made no sense...and in the context of the Cold War actually makes even less sense. The US government discovers that mutants exist. it hires some of them...who show that they have the ability to find other mutants and recruit them into working for the US government. They put them into the field, they stop a war and then that same government decides to KILL THEIR OWN AGENTS FOR NO REASON. They had not gone rogue, they'd proven their value in the field by successfully infiltrating the Soviet Union...yet they turn on them for no reason. That plot development needed to be fleshed out more. I get that in the Marvel universe people think superpowers are scary instead of cool...but this was just illogical.
3) How is Xavier "hiding" by opening a school at his FAMILY HOME?