After the musical number "Romeo and Juliet," when the Lecturer is holding the Bible and moves it out of the shot, you can hear the sound of the book landing on the grass, like it was tossed down. In the next shot, the Lecturer is again holding the Bible under his arm.
When Jimmy is holding the glasses and pointing his finger at Mary and the camera switches, his hand is back on the glasses again, and then off again.
During the song "The Stuff" Ana Gasteyer looks out the window and sing the line "Rapes Me". Before she looks out the window, her cigarette is in her left hand. It then switches to the right as shes singing out the window. When we see her again back inside the window, the cigarette is back in her left hand.
While it is indeed true that FDR was wheelchair-bound by polio, he had perfected his ability to walk with the support of someone else's arm and could stand upright for a long period of time. He never appeared in public in a wheelchair, and in fact it was not even known outside his circle of associates that he was wheelchair-bound until after his death.
In the movie FDR delivers a Presidential pardon to Jimmy. In reality, the President doesn't have the right to issue a pardon for a crime under state law, such as murder.
After the shooting, as Jimmy lies on the floor regaining consciousness, there's a clear shot of the white jockey shorts he has on under his boxers.
The story takes place in 1936, yet the Buick convertible seen during Jimmy's introduction where the Lecturer is a crossing guard is a 1938 model.
Unlike elsewhere, the flags flying on Roosevelt's car near the end are not 48 star flags but are probably 50 start flags.
The lecturer at times insults the president in front of the school parents watching the film for being weak and inefficient when dealing with drugs even though the same movie ends with FDR declaring to fight the drug menace.