Hey, It's That Guy!: While none of the other actors went on to be quite as famous as Tom Hanks, Wendy Crewson (who played Kate) would go on to play Scott Calvin's ex-wife in all three of The Santa Clause films. Chris Makepeace was a rising child actor at the time the film was made (hence why he has top billing in the actual film), having played Rudy in Meatballs and the leading role of Clifford Peache in My Bodyguard before this. Makepeace never really broke into a successful career, however, and has retired from acting.
Lieutenant Martini is played by Murray Hamilton, who played Amity Island's mayor in the first two Jaws movies.
Old Shame: Tom Hanks, as he hadn't quite broken out of television yet. Of course, since he still had The Money Pit in his future at the time of this film, he'd have some more shame to go around.