Continuity mistake: When Columbo is eating his chili in the booth at the diner, whilst talking to the daughter of the murderer, his bowl of chili moves. It is right in front of him at one point but is then away from him. And it now contains less food.
Factual error: In the series, Columbo does not carry a gun, and in several episodes it is mentioned that he doesn't like guns and/or that he doesn't know very much about them. In the real world, all LAPD officers must carry guns, and they must re-qualify with them at the range six times each year. Also, due to the very nature of their work, they are knowledgeable about numerous types, makes, and models of guns.
Short Fuse - S1-E7
Continuity mistake: When Buckner's car leaves the chemical plant, it's a stretch limo with three bench seats. When it explodes on the mountain road a few scenes later, it's only a two-seat limo. (Buckner, who was initially in the distant rear seat, is suddenly close enough to reach up and take the cigar box the chauffeur hands him from the front seat. The entire middle section of the limo has disappeared.) (00:13:40 - 00:15:30)
Factual error: Columbo gives another detective $5 to go to the gun range for him. Technically, that is a bribe and it would cost both Columbo and the other detective their badges.
Continuity mistake: Towards the end of the episode when Columbo is about to expose the killer he asks the conductor and his wife to adjourn to the recording studio from the stage. When his wife walks off the stage she has one hairstyle, but when she enters the recording studio she has a completely different hairstyle.
Factual error: To make a call, Mr. Bremer enters a seven-digit number on a push-button telephone. The first three keys he punches are 1, 2 and 4. No telephone number in the United States begins with a 1.
Factual error: Rakman Habib's driver's license shows that he lives in "Beverly Hills CA 91605." That is the ZIP code for North Hollywood, not Beverly Hills.
Continuity mistake: When Columbo and the woman have finished flying in the light aircraft, she taxis the aircraft back and shuts down the engine. There isn't much to see behind the aircraft at this point, but when Columbo and the woman get out (in the immediate next shot) there are two rather large buildings/hangars which have magically appeared right behind the aircraft. Plus the aircraft propeller has changed to a more horizontal position.
Character mistake: The policeman gets the bag for the ransom from the wife of the kidnapped person, grabs it with bare fingers and puts the money into it - without gloves, too. (00:23:30)
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. (00:43:00)
Deliberate mistake: Beth shoots Bryce three times in the chest, and he falls face down on the floor. She then drags his body across the floor, also face down, to in front of the sliding door, but there is no sign of blood anywhere.
Suggested correction: In the early Seventies, no television show used blood effects. They were too expensive and would severely restrict potential audiences as television channels were notoriously conservative in those days. This is a creative and technical decision, not a mistake.
Dead Weight - S1-E4
Plot hole: How did the revolver get into the museum after the murder? Falk said he did not see it in the packing crate.
Factual error: Near the end of the episode, Jackie Cooper fires a bullet into his hotel room from the balcony using a revolver fitted with a silencer. Hayward also uses a revolver with a silencer to kill Stone. This is a classic Hollywood error, as silencers do not work on revolvers (unless noticeably modified), due to the gap between the barrel and the cylinder. They also don't make gunshots nearly as quiet as shown.
Continuity mistake: The insurance agent has a complete hot dog in his hand while Columbo talks. When we cut to a view over his shoulder, Columbo's sentence continues but the agent is suddenly chewing. When did he take that bite? (00:36:20)
Character mistake: In the performances, Benedict is not conducting; he is waving his arms around.
Factual error: When Mrs. Williams takes Columbo flying, she does some aerobatics. Neither of them is wearing a seatbelt. No pilot would do that.
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."
Character mistake: During a rehearsal, conductor Alex Benedict instructs the orchestra to play "quasi un fantasia." Columbo asks Benedict's wife Janice what those words mean. She tells him, "It's Latin for 'like a fantasy." The words are Italian, not Latin.
Death Hits the Jackpot - S11-E1
Continuity mistake: After Lamarr takes off Freddy's undershirt we see the level of the water in the bathtub. Then he drags Freddy over to the tub and breaks his watch. At that time the water level is lower than it was before, even though the water was still running.
Revealing mistake: At the end when Laurel and Hardy are licking Columbo, a substance is caked on Columbo's neck, presumably the food they used to get the dogs to lick Peter Falk.
