It's not even really that good a murder scheme. For some reason they treat the magician's code of silence as some kind of sacred oath that means Santini can refuse to give Columbo an alibi. Ummm, he's not a priest or a psychiatrist. So the first hour pretty much wastes time with Columbo trying to figure out where Santini was. Then the murder just boils down to, "Well, this waiter can testify that I was in my office." What if the waiter was so sick of losing a bet every night for umpteen billion weeks that he decided to lie and say Santini wasn't there? Especially over a junior high school-grade trick. What if Jerome had told anyone about his knowledge of Santini's past? What if he left a "in case of my death" letter revealing Santini's secret?
Jack Cassidy can play haughty arrogant murders in his sleep and he kinda does. It isn't a particularly well-rounded performance of his, certainly not compared to "Murder by the Book." The character of his daughter is kind of a waste, and gets tossed overboard. What does she think of having a Nazi as a father? Is he really concerned about her and her boyfriend, or is Santini just being a jerk?
The bits with Columbo and the raincoat (and telling Dog to "not" guard it) are cute, and his relationship with Wilson is funny. But overall this seems to be a fairly week mystery with weak characterization.