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.
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: 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.
Visible crew/equipment: The Great Santini makes a vase of flowers appear on a table. Before he holds up a cloth to conceal the vase as it appears, the tips of the flowers can be seen beyond the far edge of the table. As he pulls the cloth away, there is a quick glimpse of the hand of the crew member who put the flowers on the table.
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.
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: 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.
Continuity mistake: Columbo is eating with the commandant of a military academy. Columbo has carrots on his plate, among other things. A few shots later, the carrots have been replaced with beans. The next time the plate is seen, it has carrots on it again. Later on in the same scene, the beans are back. Finally, at the end of the scene, there is a longer shot as the commandant is leaving the table, and where the vegetables were there is now something that looks like meat.
Plot hole: When Columbo tries to explain the position of the cars and the angle of the shot, he gets to the version when they come to the conclusion that if the car behind the other car park one way than the first car wouldn't block the light, so the shooter could see the victim. Colombo says it is possible, but in that case it wouldn't explain the angle of the shot. However there could have been 2 shooters which would instantly answers the question, and Columbo wouldn't come to the conclusion that it was a mistaken identity case.