Plot hole: Unless Jarvis Goodland has the world's most stupid lawyer, he has nothing to worry about. Columbo searches the greenhouse and uses a metal detector to find the bullet which, supposedly, shows Goodland's gun is the murder weapon. He conducts the search without a warrant and against Goodland's wishes - he asks him several times to desist with the search and leave. Any evidence discovered or collected during the search is inadmissible in court.
Plot hole: Jarvis Goodland, who grows orchids in a greenhouse, shoots and kills his nephew. A year earlier, Goodland had fired a shot at an intruder who was attempting to steal some orchids. The shot missed and went into the dirt of a flower pot. Columbo finds the bullet and it helps to prove Goodland killed his nephew. A bullet fired from a .32-caliber pistol would have shattered the pot.
Continuity mistake: There are several views of Uncle Jarvis in his (beautiful) Bentley S2 Continental from the front. We see the inside rear-view mirror, and it is correct. When we see him spot the police behind him through the mirror, it is a different mirror and not the correct one for that car.
Other mistake: When Columbo is examining the crashed Jaguar, we see silvery tape around the opening where the smashed headlight had been. The tape shouldn't be there.
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