Continuity mistake: There are several views of Uncle Jarvis in his (beautiful) Bentley S2 Continental from the front. We see the inside rear-view mirror, and it is correct. When we see him spot the police behind him through the mirror, it is a different mirror and not the correct one for that car.
Factual error: Probably an in joke - the wheels of the "airliner" shown landing at LA international airport are those of a B52 bomber. They are very distinctive and look nothing like those on any airliner ever made.
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.
Plot hole: In the last scene Columbo convicts Hanlon of murder by playing back the recording of Hanlon's final call to the victim Wagner (the phone-box call near the crime scene is Hanlon's alibi. He is pretending to be in his VIP-box in the football stadium, which is too far away at the time he murders Wagner). The point is that the recording is missing the loud clock chimes from a little clock inside the VIP-box, which means Hanlon's alibi is "destroyed", he was not in his VIP-box, he must be somewhere else at that moment. Problem is the missing clock chimes are not hard evidence. Hanlon could say the clock was not working that day or the battery was empty and so on. Beside that it would be much easier to catch Hanlon if Columbo would check the outgoing phone calls asking the telephone company.
Continuity mistake: When Columbo takes the whiskey decanter out of the murdered man's liquor cabinet, he puts his cigar in his mouth with his right hand and opens the bottle with the same hand. A second later, the shot changes to a closeup of him sniffing the contents and the cigar is back in his hand. (00:28:55)
Other mistake: Several of the English characters change back and forth between calling Columbo "leftenant" and "lootenant."
Requiem for a Falling Star - S2-E5
Other mistake: Twice, Columbo tries to reach his wife via telephone. On the second attempt, he dials seven numbers but on his first attempt, he dials only five numbers.
The Most Dangerous Match - S2-E7
Factual error: Clayton tells Columbo that he had purchased a new transistor for his hearing aid. Hearing aids - even the old types in use in the 1970's - do not have any user-replaceable parts. The only thing that can be replaced is the battery.
The Most Dangerous Match - S2-E7
Other mistake: The police photographer takes a picture of the garbage grinder. His camera has a flash, and the photo is indoors, but the flash does not fire.
Double Shock - S2-E8
Continuity mistake: Columbo stands in the doorway of Lisa's balcony while he questions her, and her gold drapery catches and hangs over his right shoulder, where it remains in all the close-ups. When the shot cuts, the drapery is no longer caught on his shoulder, but is safely folded against the wall behind him. (00:32:00)
Continuity mistake: Viveca's beauty mark switches cheeks several times between shots while she talks to her assistant. (00:07:45)
Continuity mistake: Dr. Murcheson is not wearing gloves when he scrapes the women's faces. Then he goes into another room and removes a gray glove from his left hand.
Continuity mistake: Just before Viveca murders Martin Sheen, she scribbles an amount on magazine-her nailpolish is red. Seconds later after the murder with the microscope, Vera's nailpolish is a completely different color, mauve.
Any Old Port in a Storm - S3-E2
Audio problem: Pay phones always dropped your coin into an internal cash box when you finished your call. In the bar, Columbo makes two calls, and after the first, we hear the coin drop as it should. When he finishes the second call, we should hear that coin fall, too, but it doesn't. (00:34:05)
Any Old Port in a Storm - S3-E2
Character mistake: Adrian Carsini, a wine connoisseur and winery manager, pours two glasses of wine, one for himself and one for Lieutenant Columbo. Each man puts his hand around the top of his glass and begins to drink. A true wine connoisseur never touches the top of the glass. He holds the glass by the stem so the warmth of his hand does not affect the taste of the wine.
Any Old Port in a Storm - S3-E2
Plot hole: Carsini has a wine vault (with very expensive wine in it) with an integrated air conditioner. There are indeed wine vaults like that. But mostly active cooling wine vault are used by "amateur" wine lovers (who can't afford an underground cellar) but not by wine connoisseurs like Carsini. Active coolings are not very reliable. A power failure or a simple malfunction and Carsini would lose all of his expansive wines he collected for many years (like we saw in the episode). So why shouldn't a huge wine connoisseur build a cellar, surrounded by cooling soil where temperatures never rise that high? He is rich, he as a big estate, a villa, and he knows better to store the jewels of his passion adequately. Why store wines in a potential oven where high temperatures (without air conditioning) can even kill a man (his brother) in the first place? It is a far fetched and an unnecessary gambling just to have a murder-plot.
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)
Continuity mistake: During his poolside talk with Nelson Hayward, Columbo carries a large cardboard box under one arm. His coat tail is hanging straight at his side in the master shot, but when it cuts to another angle, the coat is draped over more than half of the box. (01:15:00)
Character mistake: Columbo explains to Hayward (the killer) how the accepted version of events is impossible, because when he was shot Harry Stone was standing in a dark garage and the killer could not have angled the headlights of his car in such a way that he was made visible (in order to be shot). But neither he nor Hayward even consider the possibility that the killer could have been carrying a torch, which would not only have illuminated the scene, it would have dazzled the victim and hidden the shooter.
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.
Suggested correction: He very likely will. As we've seen, Columbo is very thorough. The missing clock chimes aren't meant to be definitive proof, just enough to warrant an arrest. Columbo will continue to work the case and gather evidence.
Columbo will continue to work the case and gather evidence? Well with that sentence they could stop every Columbo episode after 5 minutes. Hey guys, Columbo has nearly nothing against the murderer but he will continue to work the case outside this episode be sure.
It's the detective's job to investigate the crime and gather sufficient evidence to warrant an arrest and potential conviction. Yes, this would apply to every episode, and yes it applies to all detectives. Many of Columbo's investigations result in him using circumstantial evidence to arrest the killer. In one episode he arrests a man based on how the victim's shoes were tied. That wasn't his only evidence, however. In many cases a preponderance of circumstantial evidence is enough.