Plot hole: In the second movie, "Ransom for a Dead Man," the detective shows Columbo the ransom dropping place on the map sent by the kidnappers - but the detective is touching the map without gloves.
Continuity: In the psychiatrist's office, Columbo strikes a match and lights his cigar. Two seconds later, we switch to a closeup shot and the match is about six inches away from his cigar, which he proceeds to light again.
Plot hole: The policeman gets the bag for the ransom from the wife of the kidnapped person, grabs it with bare fingers and puts the money into it - without gloves, too.
Plot hole: In the second movie, "Ransom for a Dead Man," the cops tow in the car of the 'kidnapped' victim looking for fingerprints. But right before that nearly everybody in this room touches the ransom note and the envelope with bare fingers.
Audio problem: In the first movie "Presciption : Murder," there is a scene where the mistress of the murderer enters his bureau. You see her push the door closed while hastening through. You can hear the door lock click - but a half second too early. Her push wasn't that strong.
Continuity: Episode S01-01, "Murder by the Book": The witness dunks the strawberry in the white sauce while talking. We cut to a view in front of her, and the dialog continues but suddenly the strawberry is half-eaten. When did she take that bite?
Plot hole: In the second movie, "Ransom for a Dead Man," the case is very easy to solve - the murdering woman puzzles the text of the ransom note together with bare fingers - no gloves.
Continuity: Episode S01-01, "Murder by the Book": The insurance agent has a complete hot dog in his hand while Columbo talks. When we cut to a view over his shoulder, Columbo's sentence continues but the agent is suddenly chewing. When did he take that bite ?