Continuity mistake: 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.
Continuity mistake: When Spartan and Phoenix are fighting in the sewers, Edgar Friendly shoots his gun at Phoenix and you see the catwalk that Phoenix was on tip to its side and Phoenix dropping down to the ground with the plank of the catwalk right below him. When Phoenix lands on the ground the plank is nowhere to be seen. It should have been right below him.
Trivia: 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.
Trivia: The 'particle gun' that Phoenix picks up in the museum is actually a prototype of the real-life Heckler&Koch G11 rifle, the first gun ever to fire caseless ammunition. The gun and its ammo were developed in the Cold War to save the expenses for the cartridge case production. It was tested and modified for field use, but with the collapse of the Soviet state (which ended the Cold War) in 1991, the production program was cancelled.