
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.

Murder with Too Many Notes - S13-E4
Visible crew/equipment: When Columbo accompanies Sidney Ritter downstairs to see the elevator that goes to the roof, they are alone, but as Ritter says, "I can't think what use this could be to you," the abdomen (with hand in pocket) of a crew member, wearing a blue shirt and brown pants, is visible at the right side of the screen. (01:07:10)
Continuity mistake: When Columbo is talking with a cadet, Columbo says that he was in the army. Later, when the Colonel mentions 2200 hours, Columbo asks him what time that is. If Columbo had been in the army, he certainly would have known that 2200 hours is 10:00 PM.
Continuity mistake: Columbo wears a tuxedo the entire episode. Hours after his nephew's wedding ceremony, when Columbo's at the police station investigating the bride's abduction, his bow tie is hanging loosely around his neck. Shortly after, as he and the other detectives rush to the photography studio, the bow is now properly tied. This situation was too dire to bother redoing it, nor does Columbo ever worry about his appearance.
Continuity mistake: There are several views of Uncle Jarvis in his (beautiful) Bentley S2 Continental from the front. We see the inside rear-view mirror, and it is correct. When we see him spot the police behind him through the mirror, it is a different mirror and not the correct one for that car.
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.
Factual error: Several times, the revolver used to murder the singer is referred to as a "Weatherby" or "British Weatherby." Weatherby is an American manufacturer of rifles and shotguns; they do not make handguns. The revolver used is a Webley, which is of British manufacture.
Continuity mistake: At the cafe when Columbo talks with the police officer his cigar is in his hand in the back shots but disappears in the front shots.
Character mistake: Kingsley carries a briefcase in to the attorney's office, but leaves without it.
Caution: Murder Can Be Hazardous to Your Health - S10-E2
Continuity mistake: When Sheba the dog scratches Anders' car her claws are on the glass and the top of the metal part of the door, above the character line. In the photo that Columbo shows, the scratches go much further down the door.
Character mistake: Columbo took the Beretta off the gun display by inserting a pencil into the barrel of the gun. In a previous episode, he said to NEVER insert a pencil there because it will ruin the groove of the barrel, making it impossible for ballistics to get a match on the bulletin. When using a pencil, Columbo picks up a gun up near the trigger.

Character mistake: When Columbo is in Mr Benedict's house with Mr Benedict, he calculates the cost of Mr Benedict's house at $720,000. A moment later Mr Benedict asks Columbo; "How did you arrive with that figure, $750,000?" (00:43:20)
Continuity mistake: Just before Viveca murders Martin Sheen, she scribbles an amount on magazine-her nailpolish is red. Seconds later after the murder with the microscope, Vera's nailpolish is a completely different color, mauve.
Character mistake: Twice, Brenner refers to the T-33 aircraft as the Silver Star. The name of the T-33 was the Shooting Star.
Other mistake: In the dart scene, Columbo needed 66 to win, he missed his first two darts so only has one dart left, he hit the 25 or bullseye which is 50 but somehow wins.
Answer: In the show, he was already a Lieutenant. A promotion would put him in the next rank up, which for the L.A.P.D. would be Captain. However, some of a Captain's duties would be overseeing other officers and ensuring they're compliant with policies, regulations, and standards. It would also most likely take him out of the field. This is something Columbo has no desire for as he rarely goes to police HQ's. Nor does he show interest in compliance and standards (for example, not going to his semi-annual evaluation at the firing range). However, he could still be assigned to a higher pay grade based on expertise, which is a form of promotion that does not include rank advancement. This would be going from Lieutenant I to Lieutenant II. I don't believe in the show it's ever started what his pay grade is. Although, in s02e01 (I believe) he mentions making $11K a year. Whether or not this was a true statement on his part, if you could find pay scale information for an LAPD Lieutenant in the 70's, it could give you an idea of his pay grade.
Bishop73