In one of the establishing shots of one of the ships, a fake asteroid clearly bumps into the model ship.
Part of the spacesuits that Wayne and Lennon wear are clearly just motorcycle helmets.
At various moments, you can tell that Laura San Giacomo's recordings were done after the scripting of the rest of the movie had already finished. Lee Arenberg's character, Noel, who is working to solve her Shakespeare quotes, refers to her as "pal" at one point and also says, "May the best man win" about her. This implies that this "character" San Giacomo was playing was originally supposed to be a male. Further proof of this is that Noel and the recordings of Goad (San Giacomo) are never shown on screen at the same time.