When Dr. Okun is about to unlock "the vault", and says, "The freak show," a crewmember wearing a black and white striped shirt is hiding under the vault's floor, right behind Okun. (Only visible on fullscreen DVD.)
When Steven and David are being chased out of the alien mothership, David says "Must go faster, must go faster." This is a line Jeff Goldblum said in the film Jurassic Park (1993), when he was riding in the back of a jeep, getting chased by the T-Rex. That line from Jurassic Park was loved so much by ID4 filmmakers, they looped it into the dialogue. Jeff never actually spoke that line when ID4 was being filmed.