Character mistake: The policeman gets the bag for the ransom from the wife of the kidnapped person, grabs it with bare fingers and puts the money into it - without gloves, too. (00:23:30)
Continuity mistake: In the living room of their home, Lesley Williams shoots her husband in the chest. As he falls, he knocks a lamp off a small table. Lesley puts the lamp back on the table, but in all the following scenes in the living room the lamp is gone. (01:00:00)
Character mistake: Piloting a helicopter, Leslie ends a radio conversation by saying "Over and out." "Over" means "I'm done talking; please respond." "Out" means "I'm done talking and I'm ending this communication." An experienced pilot would never say "Over and out." They are two different terms.
Continuity mistake: When Columbo is eating his chili in the booth at the diner, whilst talking to the daughter of the murderer, his bowl of chili moves. It is right in front of him at one point but is then away from him. And it now contains less food.
Continuity mistake: When Columbo and the woman have finished flying in the light aircraft, she taxis the aircraft back and shuts down the engine. There isn't much to see behind the aircraft at this point, but when Columbo and the woman get out (in the immediate next shot) there are two rather large buildings/hangars which have magically appeared right behind the aircraft. Plus the aircraft propeller has changed to a more horizontal position.
Factual error: When Mrs. Williams takes Columbo flying, she does some aerobatics. Neither of them is wearing a seatbelt. No pilot would do that.
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