The set of the sitcom (the lavish Nutt Hotel) was actually the set built for the movie Big Business (1988). The producers of the movie couldn't get the rights to film inside the actual Plaza Hotel in Manhattan, so had it recreated on sound stages, and built "The Nutt House" around it to try and recoup construction costs. Unfortunately, it proved an expensive flop.
Co-creators Mel Brooks and Alan Spencer first met when the latter snuck into the set of "Young Frankenstein" as a teenager, just to meet Marty Feldman. Brooks however, did not know Spencer was the same person he met on set after they begin working on the show.
Co-creators Mel Brooks and Alan Spencer attempted to convince NBC not to use a laugh track, but failed.