According to one of the trailers for this film, "We don't care if you blab about the beginning of this picture; nor do we care if you give away the ending; but we do care if you reveal the middle. In fact, Jerry Lewis urges you to see this picture from the beginning, on penalty of losing your popcorn privileges." This spoofs Alfred Hitchcock's dictum that Psycho (1960) had to be seen from the beginning and his insistence that no latecomers be seated ("not even the [theatre] manager's brother").
In one of the DVD commentary, Jerry Lewis revealed that he received a lot more fan mail addressed to Buddy Love than he did to Professor Kelp. This made him feel that he should have made Love's character more evil than just obnoxious.
It was widely believed at the time that the nutty professor's sleazy alter ego, Buddy Love, was a satirical swipe at Jerry Lewis' longtime partner, Dean Martin. Though there may be some validity to this it's also obvious that Lewis was doing Frank Sinatra when he was speaking, e.g. his addressing the audience at the prom before he begins regressing back to Kelp.
The entire production was filmed from October 9 to December 17, 1962, mostly on the campus of Arizona State University in Tempe, Arizona.