Adrien Brody really had braces put on his teeth for his role as Harry, rather than get fake ones put in every day. He realized this was a mistake when he realized that he couldn't get into a fight at a bar because his upper lip would be destroyed by the braces.
Adrien Brody was asked to sign a document clearing director 'Richard Shepard' and producers from lawsuits if Brody's teeth were damaged from the braces he wore during filming. Brody refused to sign, claiming he didn't want to sue anyone, but if his teeth were ruined during filming, he would have to sue.
The trivia item below may give away important plot points.
Adrien Brody uses a knife at the end of the movie to cut Maura Tierney's character free from her restraints. This knife actually belongs to Adrien and has made its way into Summer of Sam (1999) as well.