Other mistake: In the home of a murder victim, Columbo presses the telephone's "redial" button to see who was called most recently. A seven-digit number is displayed but only six beeps are heard as the number is redialed. Later, attorney Oscar Finch places a call by dialing only five numbers.
Continuity mistake: At the end, when Columbo is demonstrating on the mannequin, his cigar changes position between shots.
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.
Continuity mistake: Columbo stops Mr. Finch on the road after following him from Biltmore hotel; as Columbo is speaking with him, the cigar in Columbo's hand is always in Finch's shot, even after we see Columbo place his hand on the roof. Plus after we see him put his hand down, the cigar ash keeps going from 1" to nothing. (01:44:20)
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