Plot hole: Dr Kepple is finally caught when he rushes to the hiding place of the calibration converter that he hid in the lamp after the murder. Why is it still there? It was a great hiding place initially when the police were searching people and the building in the hours after the murder but Kepple had plenty of opportunities after that to get rid of it. It is the only piece of evidence linking him to the crime and it is in his office so you would think that his main priority would be to dispose of it as soon as possible.
Character mistake: In the grocery store scene Robert Culp sits on a display of pumpkins but there are 2 signs that say watermelons.
Suggested correction: As a retail worker of 18 years, I know that POS (signage) mistakes happen in supermarkets, for example a product is moved and the correct POS is not replaced. This scene seems to be filmed in a real supermarket meaning this is not a mistake made by the show's producers, however if this was filmed in a studio, "Character Mistake" would be the wrong category as the mistake would have been made by the set designers.
While I've never seen mislabeled items I know mistakes can happen. But since the characters aren't real, every mistake they make is the fault of someone on the crew, whether it's the actor, writer, or set designer. For example, misspellings are considered character mistakes (unless intentional), even though it would have been made by the person who created it.
Character mistake: After Columbo disturbs Dr. Kepple and his ball goes in the rough, Kepple says they are playing for rather high stakes. He picks up his ball, looks at it, and places it back on the ground. In a high stakes game, that would be cheating, and the other players would not have tolerated it.
Continuity mistake: Just before the end we see a slide of Columbo looking at the lamp, but in the next shot of Columbo the slide is reversed.
Other mistake: Over a public address system, Cahill tells his staff to quit working on their World War III scenarios until "after lunch." He immediately returns to his office and the wall clock shows the time as 4:30.
Character mistake: Tommy Brown (Johnny Cash) broke his left leg. Throughout the show, he uses his crutch and then his cane on the left side. It should be on the right (opposite) side.
Revealing mistake: In the opening scenes, it's pretty clear that the "corpse" in the bright red dress is breathing. (00:02:20)
Factual error: Columbo parks across the street from a house where a murder has occurred. The address is given as 1278 Fairfax Drive. Columbo investigates and returns to his car. A house number, 400, is painted on the curb. The house across the street from 1278 would have an odd number, probably 1277 or 1279. It would not be 400.
Character mistake: Columbo drives to a car lot to question salesman Charlie Shoup. Admiring Columbo's Peugeot, the salesman says, "We don't see many of these. What's it got on it? 20,000 miles? 30,000?" When Columbo tells him "100,000," he replies, "Well, I don't care what's on the speedometer." He meant to say "odometer."
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
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: 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 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: 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
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.
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.
Plot hole: When Columbo presents the flipped photograph to Dick Van Dyke in the final scene, Columbo insists it is correct and proves DVD guilty. But Columbo already showed him the rejected fireplace photo, which shows the room arranged correctly. It also shows the victim's wedding ring, which would be on the wrong hand according to Columbo.
Suggested correction: It's all part of Columbo's bluff: Galesko wants to get rid of Columbo as fast as possible and believes himself to be too smart, thus falls for it. Galesko might have forgotten about the fireplace photo or underestimated its importance. Even if Galesko points out the rejected photo: Columbo is already bluffing about the first photo, he can very well just claim the second photo never existed or is destroyed too, leaving Galesko in the same position as he is before he incriminates himself.
Continuity mistake: Columbo is eating with the commandant of a military academy. Columbo has carrots on his plate, among other things. A few shots later, the carrots have been replaced with beans. The next time the plate is seen, it has carrots on it again. Later on in the same scene, the beans are back. Finally, at the end of the scene, there is a longer shot as the commandant is leaving the table, and where the vegetables were there is now something that looks like meat. (00:36:05 - 00:42:45)
