The sign on the set of his TV program says The Art Linkletter Show though he refers to it as the House Party, which was the name of his long-running daytime program.
Linkletter offers Mr. Mooney $200 if he can keep from losing his temper with Lucy for 24 hours. Mooney lasts less than 30 seconds.
Goof: When the policeman is chasing "The Fugitive" through Lucy's apartment, the camera pans too high and we see one of the studio lights above the set.
Art: Well, would you mind telling me your age?
Lucy: Not at all. Twenty-eight.
Art: Uh, would you mind telling me your real age?
Lucy: I certainly would.
A one-armed man bursts into Lucy's apartment waving a gun and saying that a guy has been chasing him for three years. This is a joke about the hit ABC series The Fugitive on which David Janssen was on the trail of the one-armed man who killed his wife.