Other mistake: In the cabin, Mrs. Danziger says he can pick up a pair of golf gloves in Acapulco. Golf gloves are normally sold as singles, not pairs. Very few people wear two golf gloves except in quite cold weather.
Character mistake: The crew of the ship is British. Most of them refer to Columbo as "Leftenant," but the doctor switches between "Leftenant" and "Lootenant."
Other mistake: The captain and the doctor play very fast and loose with medical records privacy, letting Columbo see them and discussing them.
Factual error: The nurse is smoking a cigarette in the sick bay. By 1975, when the show was recorded, that would not happen.
Factual error: The nurse brings Danziger a sedative and takes his blood pressure. She has her stethoscope in her ears backwards. A qualified nurse would not make that mistake. When she comes in after the murder to do it again, she has the stethoscope in correctly.
Audio problem: The clock striking wakes Columbo, and he gets out of bed. We see that he is barefoot. He takes a few steps in the barrack room, and we hear the sound he would make if he were wearing shoes. Then the sound gets louder and has an echo when we see him outdoors on the parade ground (in shoes).
An Exercise in Fatality - S4-E1
Visible crew/equipment: When Janus parks his car at the health spa's service entrance, the reflection of filming equipment, including a large spotlight and the location's 9-bank array lighting, is visible on the car's surface. Then Janus lets himself in with his master key. (00:10:30)
An Exercise in Fatality - S4-E1
Visible crew/equipment: While Columbo (wearing gym clothes) is in the deceased's office, he questions Janus about the barbell and other facts in the case. When Columbo walks toward the door, the overhead moving boom mic casts a shadow on the wall at the top of the screen. (01:21:40)
An Exercise in Fatality - S4-E1
Visible crew/equipment: At Tricon, Columbo calls and leaves a message on Lewis Lacey's answering machine, then he heads to the elevator and grabs his cigar. When it cuts to Ruth Stafford at the piano, as she walks toward the door a T-mark is visible on the floor; then it's visible in following shots as well. (01:00:00)
An Exercise in Fatality - S4-E1
Visible crew/equipment: After Columbo follows Janus from the beach back to the house, Janus asks the detective why he's there asking questions. Then, when Janus walks into his house, the boom mic is visible over the open door (and through the top window curtain); as Columbo follows him inside, the overhead boom mic is now visible through the curtain over the door as it pulls away. (00:47:30)
An Exercise in Fatality - S4-E1
Visible crew/equipment: At the start, while Milo Janus is in Gene Stafford's office, Janus tells him, "Calm down, stress is bad for your blood pressure," and there's a visible T-mark on the carpet where Gene stands. When Gene walks back to his chair, another tape mark is visible on the carpet near the door. (00:03:20)
An Exercise in Fatality - S4-E1
Other mistake: It is made clear that the barbell weighs 180 pounds. When we see Janus put it across the neck of Mr. Stafford, he moves it easily, as if it weighs perhaps 30 pounds. Although we know that Janus is very strong, no one could move 180 pounds that easily.
An Exercise in Fatality - S4-E1
Plot hole: When Columbo finds Stafford's street shoes in his locker, they are tied. How did Janus get his shoes off without untying them? If Janus did untie them, why did he retie them before putting them in the locker? And why didn't Columbo wonder why someone would take off his shoes and tie them before putting them away?
Suggested correction: I'm not sure how this is a mistake. I always take my shoes off without untying them.
I can't take off my lace shoes without untying them. How do you do it?
Guessing by them not being tied too tightly. Depends entirely on how much give is in the shoes or the laces - it's certainly not unreasonable.
Factual error: Probably an in joke - the wheels of the "airliner" shown landing at LA international airport are those of a B52 bomber. They are very distinctive and look nothing like those on any airliner ever made.
Factual error: Devlin proclaims himself to be a staunch Irish Republican but he refers to the Northern Irish city of Derry as "Londonderry." This is the name imposed upon the place by the British and is despised and rejected by Republicans. Devlin would refer to the city as "Derry."
Factual error: In common with many other episodes, Columbo and all the other police officers at the crime scene hopelessly contaminate it - none of them wear gloves or protective clothing. Not one artifact recovered from the scene would be usable as evidence.
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.
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: 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.
