Factual error: The murder is solved based on the time the Chinese pulled out of the Olympics. (The episode was from 1975, so it must be the 1976 Olympics.) The Chinese never pulled out of the Olympics or threatened to do so. Taiwan was kicked out of the Olympics by Canada, but Columbo mentions that it was Peking, that is, Communist China.
Factual error: Columbo gives another detective $5 to go to the gun range for him. Technically, that is a bribe and it would cost both Columbo and the other detective their badges.
Factual error: Rakman Habib's driver's license shows that he lives in "Beverly Hills CA 91605." That is the ZIP code for North Hollywood, not Beverly Hills.
Factual error: All LAPD officers must re-qualify with their weapons multiple times a year. If indeed Columbo could not "hit the target," as he says to another detective, he would never have made it through the police academy, much less have become a detective and have been promoted to sergeant and eventually to lieutenant.
Factual error: Columbo asks for a red wine. His host orders a Beaujolais but the butler brings a Bordeaux. Beaujolais is from Burgundy, not Bordeaux. (01:18:40)
Factual error: Columbo is sent to investigate the murder of a man near the Santa Monica Pier. Santa Monica has its own police department. The LAPD has no jurisdiction there.
Factual error: Santini murders Jerome using a revolver with a silencer. Although this is one of the oldest Hollywood tropes, a silencer (properly called a suppressor) does not reduce a gunshot to a whisper; it only cuts the noise to about 110 dB, which is still very loud. In addition, suppressors do not work at all on revolvers, because most of the noise is generated in the gap between the cylinder and 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