A lot of similarities to 'The Water Engine'; a made for TV movie also written by David Mamet in which an inventor creates something special which he is paranoid (rightfully so) about maintaining the rights to (unsuccessfully, in both cases.)
When he is hung over, George Lang says, "I put a thief in my mouth to steal my brains." The line is a close paraphrase of one from Shakespeare's "Othello": "I would not put a thief in my mouth to steal my brains."
The red and white Cadillac convertible that appears in the car dealer's showroom is the same car that is stolen from an underground garage elevator by the con men in David Mamet's House of Games (1987).
During the scene in the airport near the end of the film, the fussy child drops his book in front of Joe (Campbell Scott). The book is "The Giving Tree" by the late Shel Silverstein. Silverstein was a close friend of Mamet's and the two co-wrote the film Things Change (1988).
Mamet wrote the part of Jimmy Dell specifically for Steve Martin in order to take full advantage from the comic playing against type. He was one of the first to recognize that Martin, renowned for his manic energy, possessed a deep well of seriousness which allowed Martin to portray his character as calm and in charge, which in turn made him appear menacing.
The very first shot of the movie contains the curative advice that could have prevented the con from being effective. Joe is seen at the airport standing under the sign that warns passengers to not take packages from anyone.
The Spanish Prisoner was the first of Mamet's films to receive a PG rating. Typically, Mamet's writings are renowned for their liberal use of foul language. There is not a single obscenity uttered throughout the film.