Death Hits the Jackpot - S11-E1
Continuity mistake: After Lamarr takes off Freddy's undershirt we see the level of the water in the bathtub. Then he drags Freddy over to the tub and breaks his watch. At that time the water level is lower than it was before, even though the water was still running.
Trivia: Columbo's first name is never mentioned throughout the series. However in a few episodes, such as "Dead Weight", "A Matter of Honor" and "Death Hits the Jackpot" he flashes his badge and the name "Frank" can clearly be seen.
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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