Revealing mistake: Doug has the hologram when inside the alien nuclear reactor, and a bunch of bad guys encircle the holographic image and fire at it at point blank with automatic weapons, and not one bad guy gets hit. If they encircled the 3D image, at least a few bad guys would have been hit by their own men.
Continuity mistake: When Arnold Schwarzenegger and Rachel Ticotin are being attacked by the giant drilling machine, Arnie grabs a pneumatic drill and cuts the main oil line of the machine, getting the left side of his face and his shirt doused in oil. Yet throughout the remainder of the film, there is no oil on Arnie's face or shirt.
Revealing mistake: When Quaid throws the bullet-ridden body down the escalator, you can see Richter and Helm have both been replaced by stuntmen. Their hairstyles are totally different. You can also see that the 'dead' man is still alive as he's flying through the air (slow motion helps).
Continuity mistake: When Arnie is giving his info about what his Mars woman should be like, there are two things to look at on the screen in front of him: The screen zooms in on the woman's face, cuts back to Arnie, cuts back to the screen when it zooms in on the face again. Also, look at the sequence when he's selecting her personality: "demure" is lit up before he mentions it.
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.