Character mistake: Art expert Dale Kingston describes Goya as 'the penultimate artist'. "Penultimate" has nothing to do with greatness or artistry, it means second to last, and nowhere during his speech does he indicate that Goya is 'second to last' in anything to do with the discussion. In the context he uses it the word is completely meaningless.
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.
Factual error: When Columbo initially latches onto the radio dilemma (which ultimately solves the case) the dial is tuned all the way to the left. He later tells someone that the radio is set to 'Classical 52', but an AM radio starts at 54, meaning 540KHz. There is no 52.
Character mistake: Piloting a helicopter, Leslie ends a radio conversation by saying "Over and out." "Over" means "I'm done talking; please respond." "Out" means "I'm done talking and I'm ending this communication." An experienced pilot would never say "Over and out." They are two different terms.
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 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.
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)
Continuity mistake: In the living room of their home, Lesley Williams shoots her husband in the chest. As he falls, he knocks a lamp off a small table. Lesley puts the lamp back on the table, but in all the following scenes in the living room the lamp is gone. (01:00:00)