Factual error: When asked by the Princeton interviewer what he plans to major in, Joel replies "business." Princeton does not offer an undergraduate degree in business.
Factual error: Tom Cruise smokes a few times in the movie. He has a pack of Marlboro regular which normally have a brown filter, but whenever he pulls a cigarette out of the pack it has a WHITE filter, this leads me to believe it's a Marlboro light coming out of a Marlboro regular package, to protect his film-star lungs.