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.
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.
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.
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.
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.
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?
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.)
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.