The portrait of Mrs. Melville, the fictional detective of the Franklin and Ferris mystery novels, prominently featured in Murder by the Book (1971), makes a cameo appearance on the back wall of the meeting room at the Sigma Society club.
One of only a few episodes that the audience doesn't see exactly how the murderer covered up the crime until the very end of the episode.
The only episode where the killer is nervously anticipating Columbo's arrival on the crime scene (that is, after he anticipates whoever the homicide detective might be). Usually it's the other way around: the killer entering the scene where Columbo already is and trying to lend a hand, giving Columbo advice (which is their undoing).