Corrected entry: In the big fight scene at the end of the movie against The Brotherhood, Storm fights Callisto (Speed/mutant-detector) and kills her via electricity which comes out of her hands. Since Storm's power is to control weather, and weather control and electric shock are two very different things, she shouldn't be able to do this (in the first movie she had to summon lightning down from the sky to use against Toad).
Corrected entry: In the scene where Rogue talks to Wolverine about going to get the cure, she reveals that her real name is Marie. In the first X-men film, Rogue introduces herself to Wolverine as Marie after he reveals that his real name is Logan therefore eliminating the need for her to reveal her name in the third film.
Corrected entry: In the second film Magneto escapes the entire prison with only the aid of 3 ball bearings. He could have easily ripped the cars apart and used them as bullets against the troops guarding Lech and hit them with 100% accuracy or even made the cars spin like tops and slam into the guards. All he did was throw cars in random directions and let Pyro light them and hope for the best. This goes beyond a character mistake, as Magneto's often been shown to make very good use of metal around him, whereas here he just doesn't bother so it benefits the plot.