Visible crew/equipment: At the end, when Sarah puts her glasses on, a light screen is reflected in them. (01:38:45)
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)
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)
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)
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: 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's flesh is burning off in the burning tanker wreckage, you can see the wire moving the Terminator puppet around. (01:29:45)
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)
Revealing mistake: When Arnie drives through the police station, the cop is just sitting there. Not only that, his skin is a lot paler. It is too easy to see that it is a dummy. (01:00:00)
Revealing mistake: During the final chase scene, Sarah loses control of the pickup and it rolls over, as it rolls you can plainly see that it has no engine. (01:26:05)
Continuity mistake: When the tanker explodes near the end, the Terminator gets out of the truck, then falls to the ground face-first, in an open area. Then he rolls over onto his back, lying prone, and stops moving. When the endoskeleton rises a minute or so later, however, it gets up as if it had been hunched over, face down - and several pieces of the truck's wreckage fall off of it as it rises, as if it had been covered by falling metal. (01:28:45 - 01:31:00)
Continuity mistake: After Kyle saves Sara from the dance club and has her in the car she tries to get out. Kyle stops her by grabbing her. In one scene he's holding her by the back of her hair, and when it cuts back to him his hand is across her chest. It goes back and forth like that. (00:37:20)
Revealing mistake: The second future war segment: During the wide shot where Kyle and the female soldier are following the HK Tank, most of the plasma shots fired from said tank seem to come from above the gun turrets and not out of the barrels. (00:18:45)
Continuity mistake: After the Endoskeleton emerges from the diesel fire look at his teeth. They're clearly metallic when he stands up and chases after Sarah and Kyle, then when he enters the factory his teeth are white enamel. Then when he's fighting with Kyle they're metal again and finally they turn white after he's blown apart. (01:31:05 - 01:34:20)
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)
Continuity mistake: After the shootout at the disco, there is a car chase. Towards the end of this chase, they turn a corner and Kyle smashes into the police car, veering it off to the right of the screen. If you look closely at Kyle's car as he hits, you can see FIVE shotgun holes in the side of the car. However, a few shots later, Arnie is firing at the same side, but there are only TWO shotgun holes in the side of the car, with Arnie just making the third hole with that shot. (00:47:10)
Revealing mistake: When Arnie is being pulled under the semi-truck, his foot is caught and the green-colored dummy leg is revealed. It can't be a special effect sock since green screening was not in practice in the early 80s. (01:23:05)
Revealing mistake: In the second 'future war' sequence where a female soldier is practically vaporised by a passing HK tank, watch her flaming remains. You can see the (exceptionally fake looking) head of the stand-in dummy tumble away from the body. (00:14:15)
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.