Dead Weight - S1-E4
Continuity mistake: Helen Stewart and her mother are boating in the harbor and are about to pass a small island. A Marine colonel goes to the nearby home of a retired general to inform him that he is under investigation for cost overruns on a government contract, Fearing that the colonel will implicate him, the general shoots and kills him near a window. Helen is looking toward the home and witnesses the shooting. She tells her mother, "We have to go back." The boat is in the same position it was in five minutes earlier.
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