The inside joke of a couple who appeared during Steve Guttenberg's inspirational speech ("There are no aliens in Florida") are Tahnee Welch and Tyrone Power, Jr., who appeared to be reprising their roles from Cocoon (1985) and Cocoon: The Return (1988), which also starred Guttenberg.
In addition to the obvious tributes to Miami Vice (1984), Crocodile Dundee (1986), and Jurassic Park (1993), there is a scene from Scarface (1983), that of the thugs with the electric saw.
Steve Guttenberg, Michael Winslow, and Marion Ramsey appeared in Police Academy (1984), Police Academy 2: Their First Assignment (1985), Police Academy 3: Back in Training (1986), and Police Academy 4: Citizens on Patrol (1987).
There are other famous quotes in this movie, like "Zed is dead. Zed is dead" from Pulp Fiction and Steve Guttenberg riding the bomb payload down out of the plane like Slim Pickens in "Dr Strangelove or, How I Learned to Stop Worrying and Love the Bomb"
Martin Kove, as Colonel Jester, says "Strike first, strike hard, no mercy", the credo of Cobra Kai of which he is the sensei.