(at around 1h 4 mins) The mathematics homework that the Devil removes from the classroom blackboard was effectively to prove Fermat's Last Theorem--a legendary problem from 1630 that was often the subject of stories about people selling their souls to solve it. The problem was eventually solved in 1995 by Andrew Wiles and colleagues (with computer, not Satanic, assistance).
There is a deleted scene that can be seen on the DVD, which shows Elliot using one of his wishes to become a rock star, playing in a metal band and using a British accent. It was cut out because of images of drug use (Elliot takes a bong hit on stage and Alison tries to kill herself by swallowing pills), foul language (Elliot says a certain four-letter word a number of times), and sexual content (Elliot and Alison start to have sex right in the back room). It can be accessed on the DVD by going to the second Special Features page, highlighting the top choice, and clicking right. A devil on Elizabeth Hurley's shoulder should light up.
According to producer Trevor Albert, the schoolgirl outfit that the Devil wore was actually owned by Elizabeth Hurley.
The scene in the classroom where Elizabeth Hurley is teaching was shot in London, England and needed a re-shoot. Due to already working on O Retorno da Múmia (2001), Brendan Fraser was only available for a day or two in between, so director Harold Ramis and his crew had to travel to England and shoot the scene.
Near the end of the film, Elliot (Brendan Fraser) is seen riding his bike up Filbert Street in the Russian Hill neighborhood of San Francisco. The bike was pulled up the steep hill by a cable attached to a winch, which was erased in post-production.