Tom Corbett asks his son Eddie, "Would Chester run out on Marshall Dillon?"
This is the movie Eddie and his father see. If you look as they round the corner, you can see the poster for the movie.
Joel: "That's Eddie, from 'Courtship of Eddie's Father'"
The title is a reference to the title of the movie.
Snob names a fictitious serial killer film The Courtship of Eddie Kemper.
Glenn Ford is watching a Clark Gable/Grace Kelly scene on TV