According to Dave Chappelle on The Oprah Winfrey Show (1986), a scene was written during filming in which his character was to wear a dress while disguised as a prostitute. Chappelle adamantly refused. The writers complained to the producers who then tried to convince Chappelle to do the scene but he still refused. According to Chappelle, he felt that it was part of a disturbing trend in which African-American men wear dresses in films.
During pre-production, the film was originally supposed to carry a hard R rating, but after deliberations, the studio had to tone down the film's script to PG-13. This meant changing the plot, dialog and characters. John August was hired as a "script doctor" to make these changes.
The police station is actually a facade that was bolted onto the Los Angeles Central Public Library. The facade itself took the production department five weeks to build and another one and a half weeks to attach to the Library.
The trivia item below may give away important plot points.
William Forsythe was in a similar situation as in this film in the Rock. In both movies he played a sympathetic law enforcement agent who let the "criminal" go or was indifferent or sympathetic to his escape. In the rock he is told that Mason (Sean Connery) was vaporized and could not be apprehended. He smiled knowing he had escaped capture by the FBI. In Blue Streak, upon learning Logan is a felon and not a cop, he smiles we he discovers Logan is just inside the Mexican border and can't be caught.