Jim Carrey was originally considered for the angry history professor, but was decided against for being too young at the time. Bob Saget was also considered for the same role, but they felt his humor wasn't abrasive enough.
In the original script, the Melon family was rather poor. Harold Ramis, who was hired to rewrite, suggested that they should be rich instead to make scenarios funnier.
Alice Cooper's song "The Great American Success Story" (on the album "Constrictor") was apparently intended to be the theme song. Its lyrics summarize the plot, and include "he don't get no respect", and the chorus leads off with the phrase "back to school". The song was not used in the film, and there is no mention of the connection in the liner notes of the album.