Plot hole: When Arnie is driving the cop car and shooting at Conner and Reese, 5 or 6 inch holes from the gunfire are shown in the door right beside Connor. If the shell penetrated the steel door (which it could easily do - and was shown to do), there's nothing inside the door or on the other side of it to stop the bullet. Connor, and probably Reese, would've been ripped to shreds.
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.
