Nicolas Cage playing Peter Loew ate a real cockroach for this film - it reportedly took three takes. He once said about the experience, "Every muscle in my body didn't want to do it, but I did it anyway."
Christian Bale had used Nicolas Cage's performance in this film as inspiration for his role as Patrick Bateman in American Psycho (2000). The characters and films share striking similarities.
Peter's strange accent is supposed to be a fake accent used by the character because he thinks he sounds more "elegant" and "smarter" (hence the literary agent job). The accent comes and goes throughout the movie and is more prominent when trying to impress people, and less in scenes with people like the psychiatrist.
The 'cockroach scene' was entirely Nicolas Cage's idea, a decision he greatly regretted later on. Cage also received a number of calls from animal rights activists about the scene and defended his actions by asking them if they could honestly declare that they'd never used a can of 'Raid' in their homes.
Much to the chagrin of director Robert Bierman and Nicolas Cage, there were some scenes removed from the film and multiple cuts of the film suggested. Cage states that those lost scenes represented some of his best work and that he longs for those scenes to be restored someday.