Billing Displacement: The Cook's level of importance to the story is arguable, though he gets mentioned first. The Thief is the villain, and the Wife is the main character. They're mentioned in the order that sounds best as a title.
The Danza: The four title characters are named for the actors writer-director Peter Greenaway originally wanted to play them. Richard (The Cook) is for Richard Bohringer, the only one of Greenaway's original choices retained in the final film. The rest are aversions: Albert (The Thief) is named after Albert Finney, while Georgina (His Wife) is for Georgina Hale. Michael (The Lover) is named, interestingly enough, for Michael Gambon, whom Greenaway eventually re-cast as Albert.
Dueling Movies: Although not by any production elements, this movie competed with Michael Moore's Roger & Me to be the first screening Roger Ebert would watch on its debut night in 1989. He watched Roger & Me in the end.