
Continuity mistake: When Kyle and Sarah leave the motel in the pickup, they ram the Terminator before they go, and you can see the bull bars on the front are damaged. When the camera shows the front of the pickup during the tunnel chase sequence, the bull bars are undamaged. (01:20:25 - 01:22:00)

Visible crew/equipment: When Kyle and Sarah escape in the pickup truck, the Terminator chases after them on a red motorcycle. The camera does lots of shots of what's behind Kyle and Sarah and what's ahead of them. When they overtake a truck, you can see headlights following and shining on the back of their pickup. These are the camera crew's lights, as the Terminator's motorcycle is too far away, and previous shots have shown there are no other vehicles around them. (01:21:40)
Continuity mistake: The Terminator loses the flesh around his left eye early on, but at mom's cabin you can see his backlit left eyelash blinking. (01:16:50)
Revealing mistake: At the end of the film, at the split second we see the ambulance workers zip up Reese in the bodybag, his right eyelid flinches a bit. (01:39:45)

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)

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. (00:48:10)
Continuity mistake: At the very beginning of the film when we see the garbage man picking up the steel bin with his forks, if you watch closely you can see the shadow of the large forks pass the windscreen, yet in the following shots the forks are lower than the windscreen. (00:03:50)

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)
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. (01:00:45)
Suggested correction: He's definitely not giggling and I wouldn't call it a smile. Maybe he's grimacing, but I seen him just wincing at the situation he's in. At best you could say he's a bad actor, but poor acting isn't a valid movie mistake that I know of.
Continuity mistake: Every shot of the semi truck shows it has single round headlights, but after it's been blown up and the Terminator falls out of the cab, you can see that the truck has now got twin round headlights. (01:28:45)
Audio problem: Early in the film, when the punks are at the park, one of them is looking through a telescope and the other one breaks an alcohol bottle over it and says "Hey, it's my turn." If we look more closely, he actually says "My fu***ing turn." (00:05:10)

Continuity mistake: When the Terminator punches through the car window, there's broken glass all around the window frame. When he closes the door, there's only a little glass around the top of the frame. (00:12:55)

Visible crew/equipment: When Schwarzenegger rises to his feet after getting blasted out the window, a production vehicle and a couple of huge stage lights behind him are visible. (00:36:50)
Suggested correction: No production vehicle is visible and that definitely is not a stage light.
There is a stage light top right corner of the screen behind a black square light blocker.

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. (01:24:30)
Suggested correction: This scene don't have cuts. In this moment, a shadow covers the face of Reese, causing confusion, but still be Michael.
Continuity mistake: When the Terminator goes to kill Sarah in Technoir, the camera does a POV shot of the Terminator looking down at Sarah, and Sarah looking directly up at him. The immediate next shot where Kyle Reese is about to shoot the Terminator shows the the position of the Terminator and Sarah is different to the POV shot we saw before. (00:35:30)

Continuity mistake: In the scene where Sarah and Kyle are escaping in the car they found in the alley after leaving the nightclub, Tech Noir, we see Arnie jump onto the hood of their car in flames. While he is in mid-air during the jump, he is on fire but as soon a he lands (the next shot) the flames are gone. (00:37:35)
Continuity mistake: When the Terminator is crawling after Sarah Connor at the end of the film there is a close up of the endo-skeleton and the hydraulic cables from around his shoulders are missing. (01:37:15)
Revealing mistake: "Dead" Kyle Reese is still breathing. (01:39:45)
Continuity mistake: In the factory, when Reese yells at Sarah to run and then turns and starts bashing at the Endoskeleton with his metal pole, if you watch carefully you can see that his fourth blow snaps one of the head supports. Yet we see a closeup of the head during his fifth blow, and the support is fixed again. (01:31:14)

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." (00:59:55)