Factual error: After the troops are mobilized to fight against the Brotherhood and guard the cure clinics, they make a big show of them turning in their M16s and other metallic items and getting their plastic weapons so Magneto can't use the metal against them. But they wouldn't have had their M16s, to begin with; you pick up your weapon after you arrive for mobilization at your unit. They would have shown up unarmed and then had the plastic weapons issued to them right after they reported for duty. (Most likely, the scene was made just to get the point across to the audience that they need to get rid of all metal and to look flashy). Prior to the President responding to Magneto's declaration of war by mobilizing the troops, the cure clinics were guarded by civilian law enforcement, not US troops.
Continuity mistake: After Magneto declares war, troops are briefly seen exiting from a bus with brown boots. As they line up, you can see the boots have been replaced with black rubber ones.
Factual error: When Magneto has moved the Golden Gate Bridge, we see the President looking at a Satellite Image of Magneto's work. In this image, Alcatraz Island is bigger and closer to the shore than it is in real life.
Continuity mistake: When Warren dives out of the skyscraper window after refusing the cure, in the shot from his POV, as he starts to fall, you can see lots of broken glass falling with him. When it cuts to the exterior shot of him falling, there is no falling glass.
Other mistake: When Magneto is overlooking San Francisco Bay (just before lifting the Golden Gate Bridge), the scene was shot on a green screen, as whoever keyed in the sky cut off the very top of his head. What's more, it shows the characters in profile with the setting sun behind them, but they are not in silhouette. What light source in San Francisco is bright enough to outshine the sun?
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 ★