Colonel Chuck Yeager, the first man to break the sound barrier, made an uncredited cameo appearance.
Sidney Sheldon's second wife, Jorja Curtright, appears as a phony fortune teller and his 70 year old mother Natalie Leeb made her acting debut in Bigger then a Bread box.
Per the title, in the game of Twenty Questions, one of the classic questions is "Is it smaller than an elephant and bigger than a breadbox?"
The phrase "Is it bigger than a bread box?" originated with humorist Steve Allen on the television game show What's My Line? (1950). When trying to guess the occupation of guests who dealt in products, this semi-serious question would help home in on the commodities.