I have a special fondness for this particular Columbo episode, though I'm not sure why. It is very good, but there have been other Columbos that have moved a little faster. This one has a few interesting twists to the plot, but what is most enjoyable is the presence of Anne Baxter as a movie star, Nora Chandler, from Hollywood's golden age who now stars in a TV series. Kind of like Loretta Young, but with an entirely different persona. Mel Ferrer guest stars also, as does the lovely Pippa Scott. Scott plays Baxter's secretary, and Ferrer is a gossip columnist who seems to have some real dirt on Nora. He's also courting Scott, which Baxter is tremendously unhappy about. Nora is also getting some pressure from the studio. Nora has a cottage on the grounds with a fountain in the back - her late husband, Al, actually ran the studio. The present bosses want to sell off parts of the land, but Nora won't sell.
Falk and Baxter are funny together. He's initially starstruck - though I can't really agree with one poster on this board who thinks he wasn't onto her. He calls his brother-in-law George and has Nora say hello to him, and there is another cute scene with Edith Head.
It's a fascinating story, made special by Baxter and her chemistry with Falk.