A Deadly State of Mind - S4-E6
Stupidity: In the final scene: Columbo lays a trap for the murderer (George Hamilton). The 'eyewitness' when Hamilton fled the murder scene was a blind man. Hamilton is aware of this. Columbo's gambit depends on Hamilton's assumption that Columbo has coached the witness to act as though he was sighted so as to convince Hamilton that there is evidence against him. In fact, Columbo has the witness' brother, who is sighted, pretend to be the eyewitness and identify Hamilton as the man he saw driving away. When Hamilton falls for Columbo's trap and, believing he is in the presence of the blind man, tries and fails to 'prove' the man can't see. By doing so he reveals his knowledge that the witness was blind, incriminating himself. The problem is, that only a minute or so previously, Columbo had placed Hamilton under arrest, and failed to read him his Miranda Rights. Considering that Hamilton's slip up is the ONLY evidence Columbo has against Hamilton, this was a spectacularly stupid move on Columbo's part. Regardless of how many officers were present to witness this, the fact is that Hamilton was under arrest and had not been advised of his right against self-incrimination; meaning nothing that he said when under arrest can be used against him.
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