Continuity mistake: When the antimatter explodes in the helicopter, the the shock-wave blasts off part of the roof inside St. Peter's Basilica, above the alter, obliterating everything below. However, in the scene where the Camerlengo self immolates himself at the altar close to the end of the movie, there is no evidence of the shock wave earlier, the candles are burning, oil lamps are lit and alter is intact. (01:54:10 - 02:07:40)
Revealing mistake: When the old couple who give Wolverine clothes are first driving towards their house, there is an aerial shot of them driving over a bridge. This is supposed to be set in Canada (drive on the right) but it was filmed in New Zealand (drive on the left). They are driving on the right but the arrow on the road is on the left side.
Continuity mistake: Near the start, the bus approaches a curve in the road. 25 seconds later it's approaching the same curve, with the same trees. (00:15:25)
Revealing mistake: Axel's badge says deputy sheriff. He is THE sheriff. Not a deputy.
Other mistake: Capt Cahill was declared dead after the helicopter he was in crashed and then taken captive. I spent almost 24 years in the military and know that if a body is not found, even though presumed dead, the official status is Missing in Action (MIA). The notification to Capt Cahill's family should have been MIA not dead.
Continuity mistake: During the sheriff interview scene with Abbey, the time is listed as 3:45am, but later in the scene, the clock reads 2:15am.
Continuity mistake: After Esther suffocates Daniel in the hospital, Kate slaps Esther in the face. The hospital staff then hold down Kate and she drops her iPhone, screen down. The iPhone starts ringing, even though the screen is facing the floor. In the next scene, it is still ringing, but with the screen facing upwards.
Factual error: When Sam speaks with his daughter on the long range phone there is virtually no delay between some questions and answers. It takes over two seconds for radio waves just to travel from the Moon to the Earth and back in a straight line. The interval between question and answer physically can't be shorter than that and realistically should be around 3 seconds or even more, accounting for additional signal relays and time needed for a person to form a statement. Same for the communication between Gerty and the Lunar employees when Sam 2 got out of his infirmary bed.
Continuity mistake: Crowe gives the girl reporter a necklace made of ballpoint pens. When Crowe leaves and she runs after him the necklace is gone. (01:47:45 - 01:48:45)
Visible crew/equipment: James Marsden and Cameron Diaz are getting ready to go to bed. They have a short conversation about turning off the Christmas tree lights. As Marsden is bending over to turn the lights out, there is a window behind him. As soon as the lights go out, you see a head start to pop up in the window. You only see the forehead of the person, then the scene changes quickly.
Continuity mistake: In the beginning of the movie, the doctor invites the two girls knocking on his door inside out of the rain because their car broke down. He gives them both water (laced with drugs). One of the girls knocks her glass over, spilling most of the water, which can be seen as the glass sits on the table. Then when the doctor leaves the room, while the two girls are talking, you can see that the glass on the table magically is filled again.