Kathleen Turner once said of this movie, "After Body Heat (1981), I got a lot of offers but none of the films were good enough. I wanted this part because it's a comedy and because the character was so outrageous. I thought if I was very brave, I could do some extraordinary things with it. It wasn't a run-of-the-mill token female role."
When Steve Martin gets the bottle of window cleaner from the trunk of the car, the brand name is listed on the bottle, too small and too briefly to be seen without pausing the film. If you pause it, you can see that the label says "Pane in the Glass" window cleaner.
Steve Martin drops a small note into the trunk of the car and excitedly says that he has gotten Merv Griffin's autograph. The note reads "Best Wishes, Merv Griffin," and it is indeed Griffin's actual autograph.
As an homage, "Hfuhruhurr", the last name of Steve Martin's character (Dr. Michael Hfuhruhurr), was used for the name of a villain named "Hfuhruhurr the Word-Bringer," abbreviated as "The Word-Bringer" for the 1987-2006 The Adventures of Superman comic series. In it, Hfuhruhurr the Word-Bringer was an alien preacher from an unknown world who, since several millennia before, traveled from planet after planet to collect brains in order to create The Union, a vast compilation of brains of all sorts of sentient species of the universe, kept alive in specialized tanks aboard Hfuhruhurr's mothership as a community of collective conscience and shared knowledge.
David Cronenberg was Steve Martin's first choice to direct this film after Martin saw Scanners (1981). However, Cronenberg turned this down because he was busy working on Videodrome (1983) and wasn't interested in making a comedy.