This movie had a lot going for it. It was well-directed, had two great leads with a lot of chemistry with one another, thrilling action sequences, an exciting villain, and a 60's era setting that gave a rich atmosphere to the movie. So what went wrong?
First, let's talk about the flaw that all the X-Men films share: they focus on a few heroes and villains and ignore everyone else. Banshee had no depth besides "Screaming Guy". Why was Havoc in prison? Darwin existed to apparently be the black dude who dies first. None of these characters had anything resembling personalities. The Hellfire Club was even worse. Besides Sebastian Shaw, there was silent henchman #1, silent henchman #2, and the White Queen who was just there for eye candy.
This brings me to the treatment of the female characters. Mystique is presented as growing up with Prof X (which wasn't mentioned in the previous movies but oh well) and the moment she has a little crush on Magneto, she no longer cares that her adopted brother has been shot in the back and is possibly dying on the beach of Cuba. She runs off with Magneto without hesitation and with little set up. Angel likewise joined the bad guys even after witnessing Sebastian Shaw killing one of her own teammates. There is little explanation as to why she would suddenly join Shaw's side outside of some CIA agents making rude comments toward her friends, which pales in comparison to someone killing her friends. Once she joins the Hellfire Club, there is no inner conflict for her character, nor is there any conflict among the X-Men. Even White Queen is quick to leave Shaw behind and hook up with Magneto. Villain or not, you would think there would be a conflict.
Next: plotholes. What happened with Magneto after Shaw killed his mother? It jumped from the concentration camp to adult Eric in South America with no explanation. Why would Hank take the untested mutant cure just before an important mission? Yes, he felt like a freak but what if the "cure" killed him? He was the only one who could fly the plane. How would Shaw's nuclear war plan work? Even if mutants can survive the nuclear fallout, there would be no planet left to live on.
It had potential though.