Deliberate "mistake": In the scene where the two boys fall from the building and the giant catches them, the boys would still be very hurt, as the giant catches them just before they hit the ground by putting his hand out, since his hand is made of metal it wouldn't do much help, in actual fact landing in the snow would be better for the kids.

Factual error: In the scene where the Iron Giant is spinning the boy around in a junk car he is holding, notice that the car resembles a 1959 Cadillac...however since the film is set around 1957, this is not a likely car to be found anywhere yet, much less a junk yard.

Continuity: When the Iron Giant first learns to talk, he picks up a huge boulder that wasn't there earlier. The boulder was in a pretty big hole, but when Hogarth walks away the hole has disappeared.