Continuity mistake: At the hospital, a guard opens a door with his club, takes it away and looks inside. From a different angle the club is still on the door.
Continuity mistake: When Dyson enters the vault, the door is open different amounts between shots.
Continuity mistake: The position of Sarah's left hand clenched on the playground fence is higher-than or parallel-to her right hand, depending on the angle.
Continuity mistake: When the Terminator arrives on earth, his position differs between the first and second shot, with his left leg protruding more/less and his back crouched/slightly raised.
Continuity mistake: When the Terminator's chopper breaks through the gates of the reservoir, they sound as if they crash against the fence, yet a frame later, from the angle in front, the gates are open wide and still.
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)
Continuity mistake: During the pool fight scene, you can see there's an orange ball next to the upper left pocket. In following shots it's no longer next to it and it has a dark ball in front.
Continuity mistake: At the steel mill, the T-1000 points his finger at Sarah and tells her to call John. The style and position of the loose hairs around her forehead change between frames.
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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