Continuity mistake: We see the Terminator remove his left eye in the hotel room and it leaves a wound about the size of the sunglasses lens, in most face shots after that while he is wearing the sunglasses the wound has disappeared and the skin around the eye is perfect when we see that side of the face.
Plot hole: When Kyle Reese first enters the picture, the police immediately start chasing him (which ultimately works to the Terminator's advantage, as he is able to use the radio chatter to track his target). But why are the police after Kyle in the first place? All he did was steal a homeless guy's pants. There's no way that would generate that big of a response from the LAPD.
Suggested correction: Hardly a plot hole to have him be chased by the police. But they saw a half-naked guy in an alley at night; that's suspicious. He stole a man's pants and ran. Then he assaulted a police officer and took his gun. It escalated pretty quickly.
Continuity mistake: When Sarah rolls Kyle's body over and looks at him, his face is covered in blood and his eyes are open. When Kyle is later zipped up in the body bag, his face is clean and his eyes are closed.




