When science teacher Bob Roberts (Dennis Hopper) returns from the 1960s, he's wearing the same costume that Hopper wore when he played Billy in Easy Rider (1969).
When the guys see the gladiator, he tells them "Morituri te salutamus" which is a Latin phrase meaning "Those who are about to die salute thee."
In a scene where John Stockwell's character is under his car fixing it, Fisher Stevens says to him: "Ya know, I seen this movie where this haunted car flames guys out.", referring to John Carpenter's Christine (1983) in which Stockwell had a major role.
According to CINEFANTASTIQUE Magazine, alien puppets were made for the opening sequence, but were scrapped.