The scene in which the horse is cut into segments suspended in glass cases is inspired by the work of British artist Damien Hirst (e.g., the installation "Some Comfort Gained from the Acceptance of the Inherent Lies in Everything").
In the scene where Catherine talks with Carl while he is "cleaning" his first victim, the scenery resembles the music video "Losing My Religion" by R.E.M.; that video was directed by this film's director, Tarsem Singh.
Director Tarsem Singh asked Tara Subkoff during her interview if she could swim, to which she responded that she could and that she had been a lifeguard. It turned out that she could not go under water without holding her nose. Singh would have switched her role with Catherine Sutherland, but it was too late and there was not enough money or time to re-shoot.
The trivia item below may give away important plot points.
The last scene of the film in the desert was originally an earlier scene in the film depicting another one of Catherine's therapy sessions with Edward. Later when director Tarsem Singh decided the film needed closure on Edward's story he had digital snow and cherry blossoms added to the scene to make it look like it was part of "Catherine's world".