Continuity mistake: At the start of the film when we first see Reese arriving, the drunk homeless guy is holding a bottle in his left hand, then the camera continuously switches between Reese's arrival and the old guy, in these shots, the bottle keeps changing hands from left to right, then back to left. (00:06:40)
Visible crew/equipment: After the Terminator arrives in 1984, he begins to walk over to a short concrete wall and looks at Los Angeles over it. A second before the shot ends, the shadow of a camera is visible to the left of screen. (00:05:05)
Visible crew/equipment: At the end, when Sarah puts her glasses on, a light screen is reflected in them. (01:38:45)
Audio problem: When the Terminator breaks into the police station, he has a Franchise SPAS 12 semi-automatic (or selectable pump action) shotgun in his left hand, and an Armalite AR 180 machine gun in his right. Before he kills the power in the building, he comes to the end of a hall, points his shotgun through a doorway, and shoots. A machine gun sound is used for the blast, instead of a shotgun sound. (01:00:28)
Continuity mistake: When the Terminator says "I'll be back" he walks out of the police station. The cop inside the building looks out of the window, looks very surprised, and you can see the headlights from the car shining on the cop's face. When we see the car just before it comes crashing through the building the headlights aren't on. In the next shot of the cop the headlights are still shining on him. (00:57:25)
Revealing mistake: There is a shot from the Terminator's POV, before he rams the blue car with the semi truck, in which you can see that the car is already damaged. No slow-mo is required to see this, but it is a blink-and-you'll-miss-it shot.
Continuity mistake: In the Tech Noir Bar, the same woman - blonde with a pink or orange dress - must have come dancing with her twin, because while she's sitting behind Sarah Connor when the laser beam is pointed at her, she's also dancing near Arnie. The T-800 moves past her when he sees Sarah Connor and moves to shoot her. (00:35:05)
Continuity mistake: When The Terminator's stolen police car is shown up close in the parking structure, the motto on the left side of it reads "to care and to protect." After the car crashes, you can see the motto on the left side again, but this time it reads "Dedicated to serve." The car's trim and position/orientation/color of the police emblem change as well. (00:45:50 - 00:50:20)
Audio problem: Towards the end of the movie, after the tanker is blown up with the terminator inside, Sarah and Kyle are relieved that he is finally 'dead'. When the terminator gets up from the huge fire in his metal form, Sarah screams twice, however when she screams the second time, her mouth doesn't actually move. (01:30:10)
Continuity mistake: When the Terminator enters the police department and he bends over to say "I'll be back" you can see through his shades and he has both of his eyes, despite cutting one out in an earlier scene. (00:59:35)
Continuity mistake: Arnold looks up Sarah Connor's address in the telephone book. The telephone book address has 4 digits, but he goes to a house that has 5 digits on it. (00:15:00)
Revealing mistake: In the second future war sequence. At the end of the HK/car chase, the gunner in the car has been replaced by a very obvious dummy. (00:19:55)
Visible crew/equipment: When the Terminator is blown up inside the gas truck and you think it is destroyed, Linda Hamilton and Michael Biehn begin to hug. In the shot where the Terminator begins to rise from the destroyed truck, look just a little to the right of Linda's head and you'll see a mans head pop up and his hands pull down on a lever that makes the Terminator rise up. (01:30:50)
Visible crew/equipment: In the police station, you see all the police officers running to get the automatic weapons. There is one shot where a red dot is seen to be following one officer (and it's sometimes on his back). No cops are facing the back of this cop, the Terminator is not around this part of the station, so it must be off the camera.
Visible crew/equipment: When Sarah and Kyle have run into the factory, the Terminator is breaking through the armour plated door. As the Terminator comes through you can clearly see the two operator guys crouching behind the model. (01:32:45)
Revealing mistake: When the Terminator goes into 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 shell - you can tell by the dimple in the center of the primer.
Revealing mistake: When the Terminator's flesh is burning off in the burning tanker wreckage, you can see the wire moving the Terminator puppet around. (01:29:45)
Factual error: Right after Kyle saws off the barrel of the shotgun in the alley, he pumps a shell into it, then again after his dream of the future in the car, then a 3rd time in the night club before he shoots the terminator. The 2nd and 3rd time he pumps it, shells should eject. They don't. (00:35:22)
Character mistake: When Kyle steals the police officer's gun and asks him what the date is, the officer replies "12th, May, Thursday". The film is set in 1984. May 12th, 1984 was a Saturday.
Revealing mistake: After Reese finishes battering the Terminator with the pipe, the Terminator strikes back at him. Just before the camera angle changes to show us the pipe dropping on the floor, we get a close up of Reese's face. It is a stunt double, not Michael Biehn. (01:35:10)
Suggested correction: I have literally just watched this scene, you can't see his eyes at all. Even with the brightness turned right up. You can see the outline of his eye sockets but no eyes. Yes, we should be able to see the red of the missing eye, but we don't know if the Terminator has the ability to turn this on or off at will. With the technology available at the time of the films release, one definitely wouldn't have been able to tell any difference.
Sorry to disappoint you, but both his eyes are visible under the shades. So yes, it IS a continuity mistake after all.