Plot hole: Columbo is in the Pauley's hotel room trying to figure out how the bottle landed upright next to his body after he was shot. Devlin - the murderer - turns up unannounced and uninvited. How did Devlin explain that he knew where the victim was staying when he was murdered? Media reports might have mentioned the name of the hotel but there is no way they would have included the room number.
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.
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.
Plot hole: Dr Kepple is finally caught when he rushes to the hiding place of the calibration converter that he hid in the lamp after the murder. Why is it still there? It was a great hiding place initially when the police were searching people and the building in the hours after the murder but Kepple had plenty of opportunities after that to get rid of it. It is the only piece of evidence linking him to the crime and it is in his office so you would think that his main priority would be to dispose of it as soon as possible.
Plot hole: Just before Joe Devlin kills Vincent Pauly in the hotel room, he picks up the Full's Irish Dew whisky bottle with his bare hands. The same bottle falls to the floor when Pauly is shot, and Devlin then kicks it over to the body. Devlin didn't wipe the bottle clean at any point, therefore it will be covered in his fingerprints, but this is never mentioned throughout the episode. There's no way the police would overlook such a basic clue.
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)
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?
Plot hole: When Columbo presents the flipped photograph to Dick Van Dyke in the final scene, Columbo insists it is correct and proves DVD guilty. But Columbo already showed him the rejected fireplace photo, which shows the room arranged correctly. It also shows the victim's wedding ring, which would be on the wrong hand according to Columbo.
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.
Plot hole: The cruise ship is sailing from LA to Mazatlan in Mexico. Looking at a map, the ship will hug the west coast on its journey therefore is never far away from land. The murder takes place on the first evening of the cruise only a few hours after setting sail by which time they won't be far from San Diego. Why didn't the captain order the ship into San Diego or another suitable harbour and let the police take over the investigation?