The segment "Nightmare" was influenced by the "Night on Bald Mountain" segment from Disney's "Fantasia" feature film & the "Sleepy Hollow" segment from Disney's "The Adventures of Icabod & Mr. Toad". The main villain towers over his minions as they dance below (in almost the same animated motion, as in "Fantasia"). At one point the villain scoops them up with his giant hand & drops them, in the same fashion. Also, the human in the scene looks a lot like Icabod Crane, with his huge hook nose & giant ears. There's even a part when the man turns his head completely around, just like Icabod does in his film. The chase between the robot & the man mimics the chase between Icabod & the Headless Horseman.
According to the soundtrack liner notes, the "Starlight Angel" short was inspired by the Steve Barron-directed music video A-ha: Take on Me (1985).
Both Akira and Tetsuo, characters from Akira (1988), can be seen at the carnival during the starlight angel segment.