Continuity mistake: Arnie has come back to the apartment after shooting his coworkers and asks Lori if this is a hallucination. He then reveals fresh blood smeared all over the palms of his hands but he had grabbed her before he asks the question. Lori is sitting in front of him without a drop of blood on her.
Deliberate mistake: While Cohagen is on Mars, he calls Richter and chides him for trying to kill Quade. Richter is in a car on Earth, yet they're having a real-time conversation, which is impossible because of the distance. [While this is true, a movie with 4 to 21 minute pauses between lines would take rather a long time].Nicki
Continuity mistake: When Quaid uses the hologram, it's a mirror image of himself. However, before he enters the reactor room full of guards, we see him put the hologram device on his left wrist. His hologram (the one all the guards shoot at) has the device on his left wrist as well, instead of what would be the right.Bishop73
Continuity mistake: When Quaid enters George/Kuato's private room in the rebel base you can see George's desk has a different arrangement from one shot to the other with Quaid's gun disappearing, a blue container swapped with a white on, the computer's screen having a cable plugged in or out and other objects moved around. (01:16:00)TheSlider
Factual error: Martian sky is very inaccurate in the movie. It is depicted as much darker and redder than it would be in real life (Mars' sky is a butterscotch color during daytime, bluish at sunrise/sunset and far brighter than in the movie). Also, both of Mars' moons are very small, asteroid-like bodies and would appear as tinny star-like points of light to an observer on the surface of the planet.
Other mistake: After Arnold kills Harry and his gang at the beginning, how did that blood splatter get on the wall behind him to his right? He shot the henchman standing in that position from the back and the other who was shot was shot standing to the left side of the wall. So there is no explanation why the splatter is there.