Continuity mistake: In the scene where Quaid and Melina are strapped into chairs by scientists, Quaid breaks out and stabs a bar into a guy's head using a downward motion. In the next shot, the bar is now coming up from the under side of the scientist's face and out of the top of his head. (01:30:00)
Factual error: When a person goes out into space, their eyes wouldn't be sucked out, their cheeks puffed, etc. They would have about 10-20 seconds of useful consciousness, when they could get back to a safe area. Even after that, they'd still be alive for about a minute, although unconscious. The only major problem that being in space for about half a minute might cause is rupturing the eardrums and possible blindness (although the eyeballs wouldn't be graphically sucked out). NASA's studies on this go back as far as the 1960's and were used by Stanley Kubrick during the making of 2001: A Space Odyssey. (00:03:50 - 01:43:20)
Continuity mistake: If you look closely at the position of Arnie's arms while still on the 3D screen, they are in a different position when he breaks through. (00:30:00)
Visible crew/equipment: When Quaid and Melina hop into Benny's cab and are being chased by Richter, watch Benny. During the shots where the perspective is from behind Benny, you can see that it is a stunt driver in the car. His head is shaved neatly, yet Benny's hair is curly and frilly all over. (01:11:00)
Revealing mistake: When Arnie blows the old lady disguise mask on Mars Immigration, they shot him and the dome crashes. Right after the soldier gets sucked out of the room, some extra comes rolling and kicks the camera. (00:47:05)
Revealing mistake: In the scene in the Mars Air/Spaceport, the troops are wearing Casio scientific calculators on their wrists. (00:43:50 - 00:46:55)
Revealing mistake: When Doug and Melina are being chased by the drilling machine, it punches through a wall. When the machine comes out again it pulls some rocks with it, a very large one hits Melina and she doesn't even flinch, obviously because it's a fake rock. The size of rock should have knocked her to the floor or potentially killed her.
Continuity mistake: When Arnie enters the hotel room on Earth, he receives a phone call from a man with a suitcase who tells him to look through the window. While Arnie is approaching to the window, we can see in the display that the mysterious man is looking to his upper right. In the next shot, when Arnie is looking through the window, we can see that the hotel room is located at the man's left side. (00:35:10)