Continuity mistake: Towards the end of the episode when Columbo is about to expose the killer he asks the conductor and his wife to adjourn to the recording studio from the stage. When his wife walks off the stage she has one hairstyle, but when she enters the recording studio she has a completely different hairstyle.
Continuity mistake: When Columbo takes the whiskey decanter out of the murdered man's liquor cabinet, he puts his cigar in his mouth with his right hand and opens the bottle with the same hand. A second later, the shot changes to a closeup of him sniffing the contents and the cigar is back in his hand. (00:28:55)
Continuity mistake: When Columbo questions her about the carnations, Janice Benedict's sweater is either off her shoulders or covering them completely, depending on the shot. (01:11:00)
Double Shock - S2-E8
Continuity mistake: Columbo stands in the doorway of Lisa's balcony while he questions her, and her gold drapery catches and hangs over his right shoulder, where it remains in all the close-ups. When the shot cuts, the drapery is no longer caught on his shoulder, but is safely folded against the wall behind him. (00:32:00)
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.