When Spartan and Huxley arrive at the cryogenics place to battle Phoenix and what remains of his gang, Phoenix sees them on the monitor walking into the building and you see Spartan on the left and Huxley on the right. The camera angle changes to an inside view and Spartan is now on the right.
Demolition Man contains several references to the novel "Brave New World" by Aldous Huxley. Sandra Bullock's character's name is Lenina Huxley, from Lenina Crowne, a main character in the book, and the author's name. Sylvester Stallone's character is also named for a character in Brave New World, John the Savage.