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."
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.
New York locations in the movie getting a special mention during the film's closing credits included The Tunnel; the Mondo Cane Blues Bar; the Man Ray Restaurant; Magickal Childe; the Apple Core Theater; the Circle-in-the-Square Theater and and The New Museum of Contemporary Art.
At first, it might seem strange behavior or over-the-top acting, but as Nicolas Cage meanders through the crowd in the club scene and up to when he attacks the girl, you'll notice he's actually mimicking the movements of Nosferatu in the original vampire from Silent Era.