The title is derived from a Bob Dylan song of the same name. In his autobiography, "Chronicles: Volume One", Dylan recalls seeing the film and gives it a positive review.
Before Quinn looks in his rear view mirror at the green car following him, three blind men walk in front of his car. This is a homage to Dr. No in which there are three "blind men" called the three blind mice, who murder Captain Strangways a friend of James Bond. Both movies were put out by MGM.
The meaning and relevance of this movie's title "The Mighty Quinn" is that it is the nickname of this film's protagonist Xavier Quinn (played by Denzel Washington.
According to Washington, a scene of him and Mimi Rogers kissing was deleted due to negative reactions from test audiences. He told The Chicago Sun-Times: "Black women hated the scene. White men hated the scene."