This movie fails where other parody movies, such as the Airplane! or Naked Gun franchises, succeed. Despite all the puns, sight gags, and cameo appearances in National Lampoon's Loaded Weapon 1, very few of the attempts at humor manage to elicit even a chuckle. While some of this can be attributed to how this movie hasn't aged well since its 1993 release, the biggest problem is that so many of the jokes are endlessly repeated, and they weren't that great to begin with. For instance, the police chief is constantly shouting at everyone, even at close proximity. This is mildly amusing the first time, but after that, the only reaction he inspires is, "Yeah, we get it."
Even with such a talented all-star cast, the movie falls short. There's a surface-level silliness throughout, but none of it's especially absurd, original, or creative. In fact, a lot of the humor is as stock as the "buddy cop movie" stock characters being parodied throughout. The result is a parody of a genre that really doesn't need to be parodied, because it's doing just a fine job parodying itself.