The Naked Gun is based on a TV series called Police Squad, though interestingly, if not already then with this new movie, the combined run time of the movies is longer than the combined run time of the TV series which only ran for like 8 episodes. The show had some really good recurring jokes including in the opening credits, there was an announcer stating the names of the stars as they appeared in the opening credits and it always included one "special guest star" who was not actually in the episode but was seen always shooting at someone off screen. The cast list for the opening credits also included in every episode "Rex Hamilton as Abraham Lincoln", again was never actually in the show. Then at the end of the credits the episode title was announced and the name that was announced was always different then what appeared on screen. Each episode would end with a seemingly freeze frame but then one person would be walking around while everyone else is frozen.
I remember a bunch of years ago Leslie Nielsen was interviewed and jokingly said they were going to make a new Naked Gun movie and call it Naked Gun 5 with the idea that they made a fourth one but didn't like it so they never released it and went straight to 5.