Corrected entry: At the scene at the public high school, there is a close-up shot of boys wearing motorcycle boots, over which they are wearing Levis with the cuffs turned up. Nobody in an American high school in the 50's would have worn Levis with the cuffs turned up, and I doubt if anyone does so now.
Corrected entry: At the end, right after the Sal Mineo character is shot by the police, the James Dean character holds up the clip to the pistol and screams "He didn't have any bullets." Wrong. The Mineo character had fired the weapon already, and had not cleared the chamber. So even though the Dean character had removed the clip, one live round was still in the chamber, ready to be fired.
Corrected entry: Corey Allen can't get out of the car because a loop on the sleeve of his black leather jacket gets caught in the door handle. That kind of leather flight jacket didn't have loops in the sleeves.