Nicolas Cage and John Travolta spent two weeks together before filming to learn how to play each other. They decided on specific gestures and vocal cadences for each character that could be mimicked.
Co-screenwriter Mike Werb got the idea for the face surgery from a friend who had a hang-gliding accident. They had to remove most of the skin from his face, reconstruct the bone matter, and put his face back on.
John Travolta asked the writers if they were making fun of him with the "ridiculous chin" line. They explained that Castor was such a narcissist that he would hate having anyone else's face.
The scene of Adam listening to "Over the Rainbow" on his portable headphones was John Woo's idea and not part of the original script. Paramount Pictures refused to finance the extra scene and John Woo had to use his own money to make that happen. He was later paid back as the film turned out to be profitable. (A similar scene can be seen in Woo's Hard Boiled (1992))
Originally Arnold Schwarzenegger and Sylvester Stallone were in mind to play the lead roles. When John Woo was brought in to direct, he decided that John Travolta and Nicolas Cage would be more suited to the roles. Other pairs that the studio wanted was Michael Douglas (who was the executive producer for this movie) and Harrison Ford, Bruce Willis and Alec Baldwin, Jean-Claude Van Damme and Steven Seagal, Denzel Washington and Wesley Snipes, and Robert De Niro and Al Pacino.
John Woo: [dove] A dove flies by before the final face-off. The final face-off took place at a church, referencing The Killer (1989), also directed by Woo.
John Woo: [back to back banter] Sean vs. Castor with an obstacle between them throwing around a few comments before the "showdown."