Revealing mistake: In the scene in the laboratory under the mansion, when Wolverine confronts Jean about Cyclops, there is a close up shot of Wolverine's hand holding Cyclops' glasses. In this shot there is a small cut visible on Wolverine's hand - his healing power should not allow this.
Revealing mistake: When Bobby and Kitty are skating on the frozen fountain, in one shot Bobby's skates can be seen to be metal covered in ice, rather than the solid ice we saw when he made them.
Revealing mistake: After Jean kills Charles, Jean's house (which is suspended in the air) crashes downwards. Watch the scene very closely, and you can see some minor slip-ups in the computer rendering that give it away as a CGI shot. For example, some of the debris on the walkway in front of the house vanishes after landing. A very small piece of debris on the walkway is also seen "popping" upwards for no reason after having sat still for several seconds. Also, right before the shot ends, a few piece of debris in front of the middle window on the roof begin to flop about before flipping upwards in defiance of gravity. There are also several other minor issues with the shot. (Jean is no longer using her powers once the house falls, so this can't explain it).
Chosen answer: Both Wolverine and Mystique's mutations cause them to age slowly; effectively the normal human body deterioration is slowed for them, giving them a younger physical age than their actual chronological age. If that mutation was removed, then the factor that slowed their ageing would no longer function, but they wouldn't abruptly "catch up" with their actual age, they would simply possess a body at their current physical age which would age as a normal human after that point. As for the adamantium lacing Logan's bones, were his healing factor removed, he might well swiftly suffer extreme levels of toxic shock, which would likely prove fatal.
Tailkinker ★