Revealing mistake: In the Special Edition of the film, in the scene where the Marines are conducting their initial search of the colony, the shot where Hudson and Vasquez enter the "negative situation" room (where they find the hamster) is obviously sped up. You can tell by how quickly Vasquez seems to move when she comes through the door.
Revealing mistake: Right before Ripley discovers all of the eggs that the Alien Queen has laid, look at Newt's fingers as Ripley is carrying her - It's obviously a fake hand. Newt is in fact a dummy in this scene, and others preceding the chase from the Alien Queen. This dummy was created so that Weaver would not get exhausted carrying a real child around for so many scenes/takes.
Revealing mistake: Briefly after landing on the planet, we see the APC trundle across the ground. The way it moves shows it is a model, every little bump makes it jump up and down. This is a shame, considering that when it is inside the facility and in subsequent shots, it looks very good.