Other mistake: At the beginning of the movie at the police station and the next morning at breakfast, it at least appears to be established that Grandma lives with Jim and his parents. After all, they had just moved from another city and Grandma was there early in the morning at breakfast time. However that's the last we see of her. She is never mentioned again nor is she there after Jim comes home from school or at anytime after the trouble starts. It would be unusual for someone to sleep through all that went on; but no one ever says anything about "being quite or we might wake Grandma up." After that scene at breakfast, she is forgotten.
Plot hole: When the first police car arrives at the observatory, the policeman there tells them that the kid (Plato) holed up in the observatory has a gun and had "wounded a kid earlier." However, when that same policeman arrived at the mansion, he and his partner only ran into Plato and then followed him to the observatory. He had absolutely no way of knowing what had happened at the mansion prior to them getting there, which is when Plato shot one of Buzz's buddies.
Continuity mistake: In the Police Station at the beginning of the film James Dean takes off his flecked jacket to reveal his spectacle case in his top pocket. As his character does not wear glasses the offending case is removed in the next scene.
Continuity mistake: In the scene when Plato is laying on the ground outside of the observatory, he is only wearing one shoe. This is stated in the movie. The foot with the shoe on keeps alternating between shots. At first his shoe is only on his left foot. In the next shot, his left foot is clad only in socks.
Continuity mistake: When James Dean reaches into his car to switch off the radio, he reaches in with one hand, but when the camera focuses in on the radio being switched off, it's his other hand that's switching it off.
