The game that is rigged with an explosive is clearly the well known game Simon that is propped with a square frame to make it indistinguishable.
The film advertised at the drive in movies when the Harts meet with the private detective is Miracle on 34th Street. This 1947 film starred Natalie Wood who was Robert Wagner's wife.
Jonathan: It's a transmitter, and someone slipped it into my pocket.
Jennifer: And I found it.
Stanley: What were you doing with your hand in his pocket Mrs. Hart?
Jennifer: I still prefer my Christmas cheer in front of the fireplace, after dark.
Jonathan: That's why I come down the chimney every night.
Jack Riley went on to be the voice of Stu Pickles on the Nick show 'Rugrats'.