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.)
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.
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.