A possible explanation for this being the only edition without a composer credit can be found in a "Knowing the Score" interview from 1975. Composer Paul Glass mentioned that he had just had a Columbo score "thrown out."
Edith Head, one of Hollywood's greatest costume designers, was a long-time friend of Anne Baxter. Along with creating Baxter's full wardrobe, Head also makes a guest appearance. Head's designer office is shown during the episode. On the desk are displayed her real seven Academy awards. She had yet to win her eighth and final award, for the movie The Sting (1973). She finished her career as the most nominated woman (35 nominations) and also the most honored woman with her eight Oscars, all for Costume Design.
The studio rear projection cut-away car used here is a Lincoln Continental MK111, originally made for the 'Dean Martin' Matt Helm film The Wrecking Crew (1968).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.
This was the only Columbo (1971) 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 trivia items below may give away important plot points.
The black-and-white film that Columbo watches for a few moments while waiting for Nora Chandler in her bungalow is homage to Anne Baxter's stalker character Eve Harrington in All About Eve (1950). The clip that Columbo watches was not from the film itself but was created for this episode.
This episode features several references to Anne Baxter's most famous film All About Eve (1950). For example, the main character's name is Nora Chandler, and in the film Bette Davis played Margo Channing. Also, her nemesis. Mr. Parks, is a columnist/critic, as is the character of Addison Dewitt in the film.
This at first appears to be (along with "A Stitch in Crime") a very rare instance of the original intended victim never being killed. However, it is determined in the end that Jean was the original intended victim all along.