Other mistake: When Benedict puts his briefcase in the back of the Jaguar, the hatch does not close properly. It is still not closed properly when he picks up the car from the repair shop.
Other mistake: When Columbo is examining the crashed Jaguar, we see silvery tape around the opening where the smashed headlight had been. The tape shouldn't be there.
Other mistake: Several of the English characters change back and forth between calling Columbo "leftenant" and "lootenant."
Requiem for a Falling Star - S2-E5
Other mistake: Twice, Columbo tries to reach his wife via telephone. On the second attempt, he dials seven numbers but on his first attempt, he dials only five numbers.
The Most Dangerous Match - S2-E7
Other mistake: The police photographer takes a picture of the garbage grinder. His camera has a flash, and the photo is indoors, but the flash does not fire.
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