Police Squad! and the first Naked Gun movie worked so well because Leslie Nielsen played it straight.
Same goes for Airplane! If you can somehow block out all he craziness, it really feels like it's a potential catastrophe. Ironically, had everyone played their scenes like a comedy, it wouldn't have worked. They were brilliantly directed to play it like a nail-biting drama.
Which confused the hell out of about half of them. Graves, Bridges, and Nielson didn't get it at all when they first started. Nielson figured it out and ran with it, eventually turning it into the career he never really had. Graves never did understand what they were trying to accomplish.
Robert Stack was the one that finally got them to understand it. At one point Bridges asked him what was supposed to be funny about this line, where's the joke, and Stack answered "Lloyd,
we're the joke," after which it all made sense to him. In the words of David Zucker "Stack totally got it."