Claudia Haro, who plays Marty (the girl who asks Simon to dance at the party), was married to Joe Pesci at the time.
When the movie was filmed in the winter of 1993-1994, there was already at least a meter of snow on the ground in Harvard Square and in all of Boston. However, because the actual snow did not look "real" enough to be filmed, it was all cleared away and replaced with artificial snow.
Six big-name British actors were in the running for Prof. Pitkannan, but Joe Pesci vetoed all of them, wanting the role to go to a big-name American actor.
This was originally set up as a Dustin Hoffman project.