Pre-production for the movie lasted just one week. The film was conceived after Larry Cohen was fired from a big budget film shooting in New York. Cohen, determined not to waste the hotel room he had paid for, hired the actors and prepared a shooting script within six days.
Writer/director Larry Cohen, according to interviews, once looked at the Chrysler Building and said, "That'd be the coolest place to have a nest." This single thought was the idea which began the creation of this movie.
In an interview on NPR's "Fresh Air", Michael Moriarty described the scene in which he auditions as a piano player. The music he played was a self-composed and unrehearsed improvisation, and the dog's reaction was genuine.
The French movie poster incorrectly shows the monster covered with feathers, a wavy dinosaur frill along its back, and with large white teeth. This is because it was illustrated and printed up before copies of the film were imported into France.
The undercover cop disguised as a mime artist is wearing an Amadeus t-shirt. This is from the popular Broadway play, which was running in 1982, and not the film version which came out two years after Q was released.
In the opening scene of the movie, a window cleaner loses his head to the monster. His name is William Pilch, and was the window cleaner for the Empire State Building at the time of the movie's filming.