One of Airplane!'s great running jokes is Ted's war flashbacks. Manifesting hilariously as grainy, black and white WWII-era dogfight footage, Ted often lapses into these memories when the going gets rough. Of course there's a particularly strong absurdist element to these old-timey images, seeing as our young protagonist likely wasn't even born at the time of WWII, and certainly never flew those kinds of planes. (Source) Before long, the footage of WWII dogfights devolves into something much more odd, a memorable taste of ZAZ weirdness.
There's no elaborate allegory or metaphor involved in this running motif; just some good old fashioned visual humor. ZAZ plays on the stereotype of the demon-plagued war veteran, using images that seem to do a sincere job of capturing his trauma, right up until you realize, "Oh, wait, those are WWII propeller planes and this movie takes place in 1980."
In this sense, like much of the humor in Airplane!, these flashbacks don't draw attention to themselves; instead, they're just there for those who pay attention and surrender to the strangeness.
P.S. Did the flashback to Ted and Elaine meeting feel familiar? That's because it's an overt parody of Saturday Night Fever.