An Exercise in Fatality - S4-E1
Other mistake: It is made clear that the barbell weighs 180 pounds. When we see Janus put it across the neck of Mr. Stafford, he moves it easily, as if it weighs perhaps 30 pounds. Although we know that Janus is very strong, no one could move 180 pounds that easily.
Continuity mistake: When Columbo is talking with a cadet, Columbo says that he was in the army. Later, when the Colonel mentions 2200 hours, Columbo asks him what time that is. If Columbo had been in the army, he certainly would have known that 2200 hours is 10:00 PM.
Factual error: Several times, the revolver used to murder the singer is referred to as a "Weatherby" or "British Weatherby." Weatherby is an American manufacturer of rifles and shotguns; they do not make handguns. The revolver used is a Webley, which is of British manufacture.
A Deadly State of Mind - S4-E6
Plot hole: Collier's relationship with Nadia Donner is wildly improper, and her husband knows about it. It seems unlikely that nothing was done about it.
Other mistake: When Rosanna's body is brought to the ship's medical room, the doctor confirms that there are no bruises on the body, but she had been forcibly slapped in the face earlier that day by Mr Danzinger (Robert Vaughn). The slap was hard enough to knock her over therefore a bruise should be visible, even through make-up.
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