Character mistake: Art expert Dale Kingston describes Goya as 'the penultimate artist'. "Penultimate" has nothing to do with greatness or artistry, it means second to last, and nowhere during his speech does he indicate that Goya is 'second to last' in anything to do with the discussion. In the context he uses it the word is completely meaningless.
Continuity mistake: Colombo is talking to Mr. Kingston in the building entry after the reading of the will. A girl with red and white striped sleeves walks out of the building. A minute later she walks out of the building again. (01:15:50)
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