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.
Revealing mistake: When Quaid throws the bullet-ridden body down the escalator, you can see Richter and Helm have both been replaced by stuntmen.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).
Revealing mistake: Pay attention to the drywall on Quaid's left just as he exits the bathroom to a rain of gunfire. If you look closely there are discolorations in the paint where explosive charges are packed and set to detonate in lockstep with the shots - creating "bullet holes".
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.
Revealing mistake: In the last scene, when Douglas Quaid and Melina are holding each other and looking over the landscape of Mars while the sky gets colored, the camera starts from top behind them (looking down) then moves down while looking at them, so more and more of the Mars horizon gets visible. But the camera-tilt goes too far up, so at the top of the picture, you can see the blue-screen curtain and the pole and rings holding it. Douglas Quaid and Melina are just looking at a blue-screen. (This is visible on the video; on the DVD an extra black top-bar is covering it.)