Appearing in "Courtship of Eddie's Father" in his film debut in the uncredited role of Child at Party in Indian headdress is Ron Howard's (Eddie) younger brother, Clint Howard. This marks the beginning of a career for Clint punctuated by appearing in film and television work that also involves his brother Ron.
In Norman Jones's (Jerry Van Dyke's) radio studio, there are black-and-white publicity photos of various celebrities on the wall. One of the pictures is of Jerry Van Dyke's real-life brother, Dick Van Dyke, who was starring in The Dick Van Dyke Show at the time the film was made.
Previously Ron Howard and Shirley Jones had played sister and brother in The Music Man while in this movie they probably become stepmother and stepson.
The film that Eddie and his father see at the cinema is Sam Peckinpah's western Ride the High Country - like this film, an MGM picture.
The movie Tom watches briefly and somewhat wistfully on TV before Eddie comes in to say he feels "real terrible" is Mogambo, starring Clark Gable and Grace Kelly.
Rance Howard:
Appearing in an uncredited role (camp counselor) is Ron Howard's father. As with Clint Howard, this was one of several times Rance would be part of a production involving Ron.