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).
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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)
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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)
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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)
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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.
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.