Egocentric actor Ward Fowler (William Shatner), who portrays Detective Lucerne on a weekly TV show, is being blackmailed by his producer and ex-paramour, Claire Daley (Lola Albright), over the fact that he was a deserter in the Korean War. Fowler drugs a friend staying at his house watching a baseball game, puts it on tape delay, then dons a ski mask and pretends to rob a delicatessen where Claire is shopping. After Fowler knocks the proprietor unconscious and takes Claire's money, he shoots her dead, then ditches the gun and mask. He begins stepping in and out of character to "assist" Columbo with the investigation.

Final clue/twist: After Columbo has shaken Fowler's alibi, he confronts him with his biggest mistake. There are no fingerprints on the murder weapon, but Fowler left his fingerprints on the remaining live bullets inside the revolver's chamber.

The Lytton family owns and operates an antiquities museum. Ruth Lytton (Joyce Van Patten) has dedicated her life to the museum, never marrying and having no children, although her niece Janie (Jeannie Berlin) is as close to her as a daughter. Her brother Edward (Tim O'Connor) is not nearly as dedicated to the family business as Ruth is; in fact, he plans to close the museum and sell the building, as it's been losing money for years. Ruth and Edward's sister (and Janie's mother) Phyllis Brandt (Celeste Holm) is a checked-out alcoholic who is likely to go along with Edward's decision. Ruth enlists Milton Schaeffer (Peter Feibleman), an ex-con who works as a guard at the museum, and whose brother Tim is having an affair with Janie, in a complex plot where Milton will steal some artifacts from the museum, fake his own death, and then flee the country while Ruth collects the insurance money. But her real goal is revealed when she double-crosses Milton during the robbery, and shoots him dead, then kills Edward when he comes to investigate the gunshot. She then plants guns on both men to make it look like they killed each other. When Ruth realizes Columbo has not fallen for the staged robbery, she tries to frame Janie for involvement in the crimes.

Bertie Hastings (Sorrell Booke) discovers that his friend, Oliver Brandt (Theodore Bikel), a senior partner in an accounting firm, has been embezzling money to support the expensive lifestyle of his beautiful wife, Vivian (Samantha Eggar). Hastings refuses to remain silent, even though he is friends with the volatile and egotistical Brandt. Brandt then plots Hastings's murder at the Sigma Society, the headquarters of a Mensa-type club for geniuses, intending to make it look like a burglary gone bad.

Final clue/twist: Columbo uses Brandt's own Mensa-level intelligence and vanity, along with his dislike of the other people in the society, to trap him. After Columbo presents a ridiculous solution to how the murder took place, specifically on how the murderer timed things so the sounds of gunshots were heard coming from upstairs, immediately followed by the sound of a falling body, an outraged and insulted Brandt shows him exactly how it was done.