Revealing mistake: When the Terminator invades the police precinct to kill Sarah, there is a part where he shoots a cop in the butt with his shotgun (right before he short circuits the building's wires). If you pay attention, the cop is smiling and giggling as he takes cover - before he is blasted.
Revealing mistake: After the Terminator (in his police car) discovers Reese and Sarah in the car park, Reese hot-wires the car and starts to speed away. After that, there are several shots of Reese driving the car. It is easy to see that it's not Michael Biehn, but a stunt double who doesn't resemble Biehn at all, and who is seen in several other shots during the movie.
Revealing mistake: In the scene were Kyle and Sarah are speeding away from Arnold in the truck, Arnold starts shooting the truck with Kyle driving. When Sarah and Kyle decide to switch (passenger, driver), the camera shows them switching but there is a stuntman in place of Kyle. If not he has gained some weight in the cheeks and grown a big mustache during the course of 2 seconds.
Revealing mistake: When the Terminator goes in to the Alamo gun store, scene of the famous "Uzi 9 millimeter" quote, the man turns to get something off the shelf and Arnold takes a shell out of the box on the counter. It is an already fired cartridge: the dimple in the centre shows it.
Revealing mistake: When the Terminator takes out his "fake" human eye, he looks into the mirror. It is very obvious it's a dummy: 1) He has unnatural movements. 2) His skin is a lot paler, and not shiny. 3) His hair style has changed. It's easier to tell in the following shot, as he looks closer to the mirror that he's changed back to "real."