These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: The Naked Gun
Adaptation Displacement: While it's more of a spin-off than a film version, the original TV series did not last very long and was not as popular as the movies, leading many people to believe that the franchise only exists as a movie trilogy.
The main theme that plays during the opening credits counts as well.
Dude, Not Funny!: There's a throwaway gag in the first film where Frank finds some old evidence proving someone was innocent of a murder, only to be told that said man was executed some time ago. It's Played for Laughs, but in real life there are instances of people being framed for murder, or a crime, and being given the lethal injection before being proven to be innocent. To some, this particular joke is kinda cruel.
"Funny Aneurysm" Moment: The repeated torment Nordberg (played by O.J. Simpson) suffers is either this or becomes even funnier, depending on your viewpoint. Especially the line that he "wouldn't hurt a fly" spoken by his on-screen wife. In the network TV version, when Frank, after unknowingly shutting down Nordberg's life support system and not noticing where the rushing hospital staff are headed, says "Just be glad you're not that guy's wife."
Basically true with all things OJ in the series.
During the cop car opening credits in 33⅓ at one point it's flying around LA and headed straight for the tallest building only to sideswipe it at the last moment. Still very disturbing.
The Jewish man and Arab man being among the feuding parties at the ballgame to embrace each other after seeing and hearing Franks emotional plea to Jane. Obviously referencing a conflict that had been raging for decades at that point...and is still raging today.
In 2½, Frank casually mentions that he and Jane are ancient history, like the Democratic party. Guess who got elected only one year after this movie came out.
Nightmare Fuel: The "Manchurian candidates" for Vincent Ludwig's plot in the first movie, who go blank-faced and robotically intone: "I....must kill....[Name]" once they're "triggered." It's fairly frightening for younger viewers - particularly when it's revealed that Ludwig's final sleeper agent is Jane!
One-Scene Wonder: Numerous examples, though John Houseman's driving instructor from the first film is a particular standout. Also, "Weird Al" Yankovic appears in all three films in this capacity.
Retroactive Recognition: Believe it or not, the woman who sings the hilariously depressing blues number in the second film is a heavily made-up Vitamin C.
Tearjerker: Frank's pleas for Jane to snap out of her hypnotic state at the end of the first film. Particularly this line:
"If you don't love me, you might as well pull that trigger, because without you I don't think I'd want to live."
While overall being very funny, the shots of everyone in the ballpark embracing because they're so moved by what they're seeing and hearing can be quite touching, especially of the Jewish man and the Arab man...and the mailman and the dog.