Continuity mistake: When the T-800 arrives between the tractor-trailers, you can see a bumper sticker (i.e. "Vehicle makes wide turns") on the back of the trailer when the sparking begins. When Arnie arrives in the bubble it "melts" out the back corner of the trailer, and the sticker is no longer there. (00:05:50)
Continuity mistake: In the shot where T-800 arrives in the time bubble, the bubble removes a clean cut chunk of the rear end of the truck. If you look at the very center of the wheel that is cut in half, there is part of the axle right at the tip of that wheel which is not cut. (00:06:25)
Continuity mistake: In the scene where the Terminator is nude in the biker bar, one biker stabs him. The Terminator then grabs the knife with his left hand and twists the biker's arm. Then the Terminator uses his right hand to hold the biker's arm down on the pool table while still holding on to the knife with his left. Immediately in the next shot, the Terminator right arm is in the air with the knife in his right hand and stabs the biker. (00:08:05)
Continuity mistake: During the bar scene, the Terminator is stabbed in the chest. You can see that he gets stabbed exactly above his right nipple. A few shots later, when he goes in the kitchen to get the biker's keys, the cut with blood dripping appears on his ribcage far below the nipple. (00:08:20)
Continuity mistake: In the bar scene after the biker burns the Terminator's chest with the cigar, it leaves a burn mark. Another biker comes behind him and hits him with a pool cue-the burn mark has disappeared, and then re-appeared in the next frame when he grabs that biker. (00:08:20)
Continuity mistake: After The Terminator exits the bar in the beginning and takes the gun from the bar owner while advancing towards the owner he takes his left hand off the barrel. From behind though, he's still gripping it. (00:09:20)
Continuity mistake: When the T-800 grabs the shotgun off the bar keeper,he cocks it (fully), then in the next shot, you see him half-way through cocking it. (00:09:30)
Continuity mistake: The scene where John and his buddy hack into the ATM and get cash, John is telling his friend his mother is a psycho. Watch closely as John puts on his backpack twice. (00:17:50)
Continuity mistake: The amount of ash on Sarah's cigarette during her review changes instantly. (00:23:20)
Continuity mistake: In the scene where the T-800 and the T-1000 have their first shootout in the mall, John Connor begins to run down a series of stairs to get to his dirtbike. Every time he passes a door it reads the level he's currently on. You will see he passes level 2 twice. (00:31:40)
Continuity mistake: During the chase scene after the T-1000 commandeers the tow truck, the shadows are inconsistent from shot to shot. Understandable, as each shot was made at different times during the day, but still noticeable. (00:32:00)
Continuity mistake: At the Galleria, the T-1000 fires rounds into the Terminator's back, but the damage to his jacket disappears when he is thrown through the window. (Director James Cameron said the scripting of this sequence at the time of filming was different). (00:32:10 - 00:32:55)
Continuity mistake: The Winchester 1887 lever action rifle is shown with different levers as the Terminator needs them. When on foot, the lever is of a standard narrow type and when on the bike, it has a large lever loop that also has a metal hand plate attached to it, making it easier for Arnold to flip-cock the gun when reloading. (00:32:20 - 00:36:35)
Continuity mistake: When the T-1000 is shot down next to the video games arcade, his face expression changes between frames. (00:32:25)
Continuity mistake: At the mall, after the Terminator has been thrown through a glass window shop, a man in grey pants approaches him from behind. When he stands up the guy has disappeared. (00:33:10)
Continuity mistake: When the T-1000 is driving the truck, he drives off a bridge and the windshield pops off, but in the next scene the windshield is back. (00:33:45)
Continuity mistake: If you watch carefully when the T-1000 has driven off the bridge in the truck, you can see the suspension and steering gear collapse and shift (severely) to the driver's right. A moment later, the alignment is perfect. (00:33:45)
Continuity mistake: When the T-1000 is chasing John in the black tow truck, after the truck goes off the bridge you can see that the truck has two tall exhaust pipes behind the cab. Then right after the truck hits the 2nd old car it shows a shot from behind the truck and the pipes are suddenly cut off. (00:34:55)
Continuity mistake: When John stops his bike at the canal, a supermarket trolley and a flat tire appear behind him. (00:35:00)
Continuity mistake: John enters the canal, passes by a bridge and pulls over 200 meters ahead. From his POV, the distance from the bridge is merely 50 meters. (00:35:00)
Answer: He didn't steal his clothes, but copied them. He can only copy things that he physically touches. He had to touch the cop to take on his look. Also since the cop was a witness to this ruthless killing machine, it needed to kill him to protect itself from being discovered too soon. The Terminator is an infiltration unit on an assassination mission to kill John Connor. As advanced as it is, it needs as little attention drawn to it as possible. Having the entire police force chasing him down would not be ideal for his goal to get Connor and would inevitably slow him down and risk allowing Connor a better chance of escape. The T 1000 also is an emotionless machine programmed by other machines that are intent on killing off all humans in the future. It doesn't value human life, and if anything has been programmed to regard them as a pest to be dealt with. The cop was a means to an ends and an obstacle to take out. As well, the cop did also posses a weapon, and was the T-1000's quickest way to get his hands on a gun.
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