This was the only Columbo music score not credited to any composer in the credit titles. The music was tracked from previous Columbo scores composed by Dick DeBenedictis and Oliver Nelson. However, both composers registered their "Requiem for a Falling Star cues" with their respective performing right societies, DeBenedictis with ASCAP and Nelson with BMI.
The studio rear projection cut-away car used here is a Lincoln Continental MK111, originally made for the 'Dean Martin' Matt Helm film The Wrecking Crew (1968). A complete car is driven by agent Matt Helm (Martin) in that film and the rear projection cut-away version has matching gold paint & brown top with red & brown interior.
Among the photos on Mel Ferrer's office wall are Jean Harlow, Lionel Barrymore, Rudolph Valentino, Sammy Davis Jr., Carole Lombard. Leo Carillo, Gary Cooper, W.C. Fields, and Carmen Miranda. There are two photos of Clark Gable.
The trivia items below may give away important plot points.
This episode is filled with little references to Anne Baxter's most famous film "All About Eve." For example, the main character's name is Nora Chandler, and in the film she played Margo Channing. Also, her nemesis. Mr. Parks, is a columnist/critic, as is the character of Addison Dewitt in the film.
The black-and-white "movie" that Columbo watches for a few moments while waiting for Nora Chandler in her bungalow is homage to Anne Baxter's stalker character in the film, "All About Eve" (1950). (The clip Columbo sees was not from an actual movie, but one created for this episode.)