Strategy X - S1-E1
Other mistake: When Nightcrawler pumps his fist in elation while standing in front of the mirror, his arm casts no reflection. (00:09:52)
Mutant Crush - S1-E4
Plot hole: With Jean's powerful telekinesis, she should have been able to untie herself from the chair.
Suggested correction: She would have to see the knots to untie them mentally. Blob could have used any number of ways to tie the rope off.
He didn't use rope, he bent a pipe around her so she should have been able to manipulate it.
Continuity mistake: In the breakfast scene, Nightcrawler teleports onto the chandelier to grab food. However, in previous shots we've seen of the dining room, there was no chandelier anywhere near the dining room table.
Other mistake: The guitar next to Rogue's bed has position markers on all of the odd-numbered frets, beginning with the first. Position markers on guitars start on the 3rd fret, and sequentially follow on the 5th, 7th, 9th, 12th, 15th, 17th, 19th, and 21st frets (and 24th where applicable).
Plot hole: In the end of the episode, Wolverine is seen recuperating after surgery removes the microchip in his brain, and his head is bandaged. Performing invasive surgery on Wolverine's brain isn't possible, since that would require going through his adamantium-infused skull and no conventional material is capable of that. Only a less invasive technique (such as going through the cranial sutres or cranial foramen) would have been effective and that most likely would not have required Wolverine's head to be bandaged (especially with his rapid healing mutant ability).
Other mistake: The trees that the brainwashed Wolverine slices down, while chasing after Kitty, fall to the ground too slowly. They should fall quickly as a large, heavy object would, but instead float down like a feather.
Continuity mistake: The claw marks Wolverine slashes through the door are suddenly longer when he exits the room.
Continuity mistake: After Rogue absorbs Blob's powers to stop him from collapsing the bleachers, the shot changes, and we see Blob falling to his knees, and Rogue standing directly behind him. The shot changes again, and Rogue is suddenly crouched down on the rubble with Kitty standing behind her, and Blob nowhere to be seen.
Continuity mistake: When Principal Kelly is placing the caution tape across the destroyed restroom wall, he applies it at a diagonal angle. When the shot changes, the tape is now at a horizontal angle, and he is now applying a second piece at a diagonal angle.
Factual error: After Alex is dragged underwater by the harness tether, Scott goes swimming after him and easily locates him. Given that they are in the middle of the ocean at nighttime during a heavy rainstorm, and Scott is wearing sunglasses, it would be way too dark below the surface to see anything.
Factual error: The map of the western United States shown during the weather report at the start of the episode shows some states drawn incorrectly. Idaho's entire western border is a straight line, whereas in real life, Oregon has a horn-shaped indentation on its northeastern border that it shares with Idaho. Idaho also looks like a crude staircase, with the southwestern border of Montana going down to central Wyoming, whereas that area in real life is around the northwestern part of Wyoming.
Audio problem: In the scene where Mystique returns to the Brotherhood house, when Pietro says that their team is as tough as ever, it's Lance's voice that comes out of his mouth.
Revealing mistake: When Wanda traps Magneto in the force field thing, for one shot, Magneto is missing a sleeve on one arm, then it comes back a shot later.
Continuity mistake: When Nightcrawler teleports into the police car, the seat belt is buckled around him. How did the seat belt buckle itself around him? The police wouldn't have buckled the seat belt for no reason.
Mainstream - S3-E3
Continuity mistake: When Kitty goes to get a midnight snack, her hair is down. But a few shots later, her hair is up in a ponytail.
Mainstream - S3-E3
Continuity mistake: During the cold open, Kitty is wearing slippers when she and Kurt fight the vandals. After the battle, she's barefoot, with no explanation as to where her shoes went.