Factual error: In common with many other episodes, Columbo and all the other police officers at the crime scene hopelessly contaminate it - none of them wear gloves or protective clothing. Not one artifact recovered from the scene would be usable as evidence.
The Bye-Bye Sky High I.Q. Murder Case - S6-E3
Factual error: A "silencer" (properly called a "suppressor") does not muffle a gunshot to a whisper. An unsuppressed gunshot is about 160 dB, equivalent to a jet airliner taking off, but a suppressed gunshot still registers about 100 dB, equivalent to a power lawn mower. Also, a suppressor on a revolver is totally useless, because most of the noise comes from the gap between the front of the cylinder and the rear of the barrel.
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