Factual error: When Wolverine is being chased after the explosion of the barn, there's a Humvee chasing the motorcycle. The movie is supposed to take place in the late 70's - the Humvee started production in 1984 and started service in the late 80's.
Factual error: When Wolverine leaves one of the compounds, he slashes through the door with both hands, creating an "X" in the door. After the second slice, the portion of the "X" where the cuts actually crisscross remains in the door, when in reality the pieces would fall out as they wouldn't be attached to the door any longer and would be floating in air. (00:44:30)
Factual error: The movie takes place six years after the Vietnam War; mid to late 1970's (if the Three-Mile Island accident depicted in the film is supposed to be the actual accident, then it would be 1979; either way, it is sometime in the 1970's). The 20-dollar bills on the ground in New Orleans have Andrew Jackson's head in the large offset oval; a redesign of the currency that wasn't issued until 1998.
Factual error: None of the vehicles in the logging camp, purportedly in the Canadian Rockies, have correct licence plates for either Alberta or British Columbia, the provinces the Rockies are located. They are not the white on blue that British Columbia was using in the early to mid 1980s, nor the black on yellow of Alberta during the same time period. They aren't even the red on white for Alberta or blue on white for BC that are currently used since the late 80s/early 90s. (00:23:40 - 00:25:00)
Factual error: During the Vietnam War scene, Logan is seen equipped with what is supposedly an XM177 Carbine/Colt Commando. Unfortunately it's not that weapon, but an M4 which was issued in 1994.
Chosen answer: Her power works by manipulating parts of the mind. Since Victor and Logan both regenerate her power can't affect them because they essentially "heal/regenerate" the part she is manipulating. Granted Prof. X threatens Logan with this in the original movies, but he is much more powerful, or could have been bluffing.