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.