When elderly physician Henry Willis (Sam Jaffe) refuses to finance a return to the spotlight for his wife, aging former movie star Grace Wheeler (Janet Leigh) kills him in his sleep, passing it off as a suicide. Their elderly butler (Maurice Evans) believes Grace was in a private screening room the entire time, watching one of her classic films.

Final clue/twist: Columbo believes that a discrepancy between the length of the movie and the time it took Grace Wheeler to watch it, including the few minutes it took her to fix the film after it ripped, proves that Grace spent some time away from the screening room. It was then, Columbo concludes, that she was out committing the murder.

This is one of the only two episodes in which the perpetrator is not arrested (the other being "It's All In The Game"), as Ned Diamond (John Payne), Wheeler's longtime song and dance partner who has always loved Grace, falsely confesses to save her after Columbo informs him she is suffering from a degenerative brain disease (the primary reason her husband refused to finance her return as the physical strain of acting would have killed her) and likely no longer even remembers the murder. Nonetheless, Columbo is prepared to arrest her. Diamond makes his false confession to Grace who briefly becomes hysterical. Columbo arrests Diamond, both realizing that by the time he is cleared, Grace will have died. Columbo's normal instincts thwarted, he makes several half turns – as though to enter the screening room – where Grace, lost in the past, is watching the film, having already forgotten Diamond's confession. Columbo then leaves the mansion, following Diamond.

The episode features excerpts from the 1953 musical comedy Walking My Baby Back Home, which starred Leigh; Colombo music composer Henry Mancini had served as the film's composer as well. It is Grace's favorite film, the one playing when she was committing the crime and the one she is watching, mesmerized, at the end of the episode.

Hassan Salah (Héctor Elizondo), chief diplomat of the Legation of Suari, an Arab nation with a new young king, has a scheme for shifting power within his government. He enlists Rachman Habib (Sal Mineo), a naïve idealist in the Legation, to help him stage the murder of a security officer, then plants evidence to make it look like the work of radicals. Salah pins the murder on the now-absent Habib, who, as part of the plan, has gone into hiding. Salah later kills Habib as well. Columbo unravels the truth, but finds himself stymied by Salah's diplomatic immunity. Columbo then meets the new king, who is on a diplomatic visit to the United States, and is liked by the young monarch.

A CIA operative code-named "Geronimo" (Leslie Nielsen) contacts a fellow CIA-operative, now working undercover as speech-writing consultant, named Nelson Brenner (Patrick McGoohan, who also directed), to demand his share of money from a previous operation they were involved in. The go-between is Otis Young. It motivates Brenner to kill Geronimo. Columbo finds himself blocked at every turn by a man who knows a lot of private and classified secrets, and even by a visit from the Director of the Agency (David White).

Final clue/twist: Brenner's alibi, a taped speech for a client, is proven false when Columbo establishes that some statements in the speech were based on news that was not known until hours after the recording was allegedly made.

Retired and renowned matador Luis Montoya (Ricardo Montalbán, credited as Ricardo Montalban) is a Mexican national hero. His trusted bookkeeper, Hector Rangel (Robert Carricart)'s son Curro is also a bullfighter. When Curro (A Martinez) is gored in the bullring, Montoya freezes up in fear and does not challenge the bull. He later decides to kill Hector, who knows what happened. Montoya lures Hector to the ring, where he shoots him with a tranquilizer gun, and unleashes the bull on the prone man. The result is that it appears Hector tried to take revenge on the bull that gored his son. Columbo, who just happens to be in Tijuana for the weekend, is recognized by a suspicious local chief of police (Pedro Armendáriz Jr.), who enlists Columbo's help.

Final clue/twist: Due to the condition of the muleta used to attract the bull, Columbo deduces the time frame of the murder, a period for which Montoya has no alibi. To prove Montoya's motive, Columbo persuades Curro to lure Montoya into the ring. The bull is then released, and the ex-matador again becomes paralyzed with fear, this time in front of witnesses. This episode is noteworthy as the murderer's motive is not revealed until the very end.

The Great Santini (Jack Cassidy) is a magician extraordinaire at a cabaret. He is also being blackmailed by his insatiably greedy employer, impresario Jesse Jerome (Nehemiah Persoff), over the fact that he is actually Sergeant Stefan Mueller, a former Nazi SS prison guard. Mueller tires of the arrangement and Jerome's demand for more money, and kills his blackmailer in the middle of his famed water tank escape act, giving himself what he believes to be an airtight alibi. He sneaks out of a room where he hides during the act, makes his way dressed as a waiter through the cabaret's kitchen and up to Jerome's office, shoots him, then returns to his act with nobody noticing. Robert Loggia plays Harry Blandford, the club's maître d' and Jerome's less than enthusiastic business partner, whose personality was such that another character says of the late Jerome, "To know him was to detest him."

Final clue/twist: Santini is undone by the used carbon ribbon on Jerome's IBM Selectric typewriter. The carbon ribbon has a clear imprint of everything written with it, so it is in effect a copy of the letter Jerome was typing to send to federal authorities, which revealed the motive for the murder. At his arrest Santini remarks that he thought he had created the perfect murder; Columbo remarks that a "perfect murder" is only an illusion.

Commodore Otis Swanson (John Dehner) is a retired naval officer who owns a shipbuilding company, and is not happy with the shady dealings of his son-in-law Charles Clay (Robert Vaughn), who has turned the modest and upstanding business into a name-brand production line for status-seekers. Nor is he pleased with any of the people closest to him - his alcoholic daughter Joanna Clay (Diane Baker), his middle-aged playboy nephew Swanny Swanson (Fred Draper), his lawyer Jonathan Kittering (Wilfrid Hyde-White), and his shipyard manager Wayne Taylor (Joshua Bryant). He announces at his birthday party his intention to sell the company. That night, someone murders the Commodore. Although we don't see the murder on-screen, Clay is seen covering up the death by taking the Commodore's body out on his yacht at night and throwing it overboard. Columbo investigates with the help of a veteran sergeant and a 29-year-old rookie. The detective's conviction that Clay committed the crime proves premature and inaccurate, an unusual development for Columbo. Clay himself turns up dead and Columbo realizes that someone else is responsible for both murders.

Final clue/twist: When Columbo holds what he says is Commodore Swanson's pocket watch to every suspect's ear, only Swanny disputes it, saying "'Tisn't" when he hears it ticking. The watch was broken at the time of the murder to create a false time frame, and only the murderer would have known the watch no longer works. (Clay's motive for covering up the murder is because he thought the killer was his wife due to planted evidence by Swanny; he was killed when he realized who the real killer was)