Other mistake: At the very beginning of the film, when the two cars are along side each other, the man wearing the hat leans out of the car window to challenge the women in the other car to a race, watch out for when he speaks, you can see that his words don't match his mouth movements - he's talking out of sync.
Other mistake: When Raymond shoots Senator Jordan, his first shot penetrates the carton of milk that Jordan is holding in his left hand. From Raymond's perspective, that carton of milk is positioned over Jordan's upper left arm; so, the first shot should have merely wounded Jordan in the left bicep, hardly a mortal wound. But Jordan's eyes roll up and he collapses as if shot in the heart.