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.
Plot hole: Unless Jarvis Goodland has the world's most stupid lawyer, he has nothing to worry about. Columbo searches the greenhouse and uses a metal detector to find the bullet which, supposedly, shows Goodland's gun is the murder weapon. He conducts the search without a warrant and against Goodland's wishes - he asks him several times to desist with the search and leave. Any evidence discovered or collected during the search is inadmissible in court.
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: Columbo discusses the murder of Jennifer Welles with Alex Benedict - who killed her - and he reveals that the odometer reading of Benedict's car showed an extra nine miles despite the fact that it was supposedly immobilised in a garage on the night of the murder. Benedict challenges Columbo, saying that he assumes that he has established the distance between the garage and Jennifer's apartment. "Yes, sir." says Columbo. "Exactly nine miles." Since the murderer would have had to have driven to and from the garage to the scene of the murder - the car was back in the garage when the police searched it the next day - shouldn't he have said "Exactly four and a half miles."?
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: 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.
Character mistake: In the performances, Benedict is not conducting; he is waving his arms around.
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.
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)
Continuity mistake: When Columbo questions her about the carnations, Janice Benedict's sweater is either off her shoulders or covering them completely, depending on the shot. (01:11:00)
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.
Other mistake: Several of the English characters change back and forth between calling Columbo "leftenant" and "lootenant."
Other mistake: When Benedict puts his briefcase in the back of the Jaguar, the hatch does not close properly. It is still not closed properly when he picks up the car from the repair shop.
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.
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.
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.
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.
Character mistake: When Columbo is in Mr Benedict's house with Mr Benedict, he calculates the cost of Mr Benedict's house at $720,000. A moment later Mr Benedict asks Columbo; "How did you arrive with that figure, $750,000?" (00:43:20)
Other mistake: When Columbo is examining the crashed Jaguar, we see silvery tape around the opening where the smashed headlight had been. The tape shouldn't be there.
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)
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.