Continuity mistake: Columbo is eating with the commandant of a military academy. Columbo has carrots on his plate, among other things. A few shots later, the carrots have been replaced with beans. The next time the plate is seen, it has carrots on it again. Later on in the same scene, the beans are back. Finally, at the end of the scene, there is a longer shot as the commandant is leaving the table, and where the vegetables were there is now something that looks like meat. (00:36:05 - 00:42:45)
A Deadly State of Mind - S4-E6
Continuity mistake: When Columbo asks if he can borrow the psychiatrist's lighter, the man has his cigarette in his mouth and a newspaper in his left hand as he reaches into his pocket for the lighter. In the next shot, as he hands the lighter to Columbo, the cigarette has jumped into his left hand with the newspaper. (00:27:40)
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