Factual error: When Columbo initially latches onto the radio dilemma (which ultimately solves the case) the dial is tuned all the way to the left. He later tells someone that the radio is set to 'Classical 52', but an AM radio starts at 54, meaning 540KHz. There is no 52.
Factual error: In the middle of summer in southern California, water spread thinly on an outdoor ceramic surface would start evaporating immediately and would be gone in about fifteen minutes. The surrounds of the pool would be bone dry by the time Columbo arrived at the scene, nearly an hour after the murderer sprayed the water there.
Character mistake: A valet tells Columbo that automobiles belonging to Sauri embassy personnel are repaired at a service station two blocks away. Later, when Columbo is speaking with Hassan Salah, he says, "I know your cars are taken to a service station three blocks away."
Continuity mistake: While riding in a chauffeur-driven car, Mr. Buckner wants to smoke a cigar. He picks up a wooden cigar box. The lid is secured by two pieces of black tape. He peels up one piece of tape. After a close-up of his face is shown, he peels up the second piece of tape and the first piece is now back in its original position across the lid.
Factual error: An important plot point is that diamonds do not burn and can be recovered from the ashes of a cremated body. This is completely wrong - diamonds would combust freely at cremation temperatures, and since they are pure carbon they don't even leave any residue.
Factual error: At the crime scene, the landlady of the dead man is brought into the room in order to identify one of the dead men. This is never, ever done - she could contaminate the crime scene in a dozen different ways. She would be asked to identify the corpse at the morgue after the scene had been cleared by forensic examiners.
Plot hole: Jarvis Goodland, who grows orchids in a greenhouse, shoots and kills his nephew. A year earlier, Goodland had fired a shot at an intruder who was attempting to steal some orchids. The shot missed and went into the dirt of a flower pot. Columbo finds the bullet and it helps to prove Goodland killed his nephew. A bullet fired from a .32-caliber pistol would have shattered the pot.
Continuity mistake: Helen Stewart and her mother are boating in the harbor and are about to pass a small island. A Marine colonel goes to the nearby home of a retired general to inform him that he is under investigation for cost overruns on a government contract, Fearing that the colonel will implicate him, the general shoots and kills him near a window. Helen is looking toward the home and witnesses the shooting. She tells her mother, "We have to go back." The boat is in the same position it was in five minutes earlier.
Continuity mistake: When Kay retrieves the gun from the elevator ceiling, they switch shots several time looking up at the ceiling and down from the ceiling. In one shot looking up, the barrel and grip of the gun are over the edge of the ceiling tile. In the next down shot, just the barrel is near the edge and the grip is inches away. Back to an up shot and the gun returns to barrel and grip over the edge.
Plot hole: (Spoiler) Mrs. Donner screams in fright just as she jumps to her death from her balcony. This seems unreasonable since she believes herself to be going for a swim (under post-hypnotic suggestion) The scream is heard by a later witness to help establish time of death. If she suddenly realized the deadliness of her act, why would she continue with it?