The series 4 episode "Negative Reaction" Columbo goes to a homeless shelter to look up a drunken witness, except the nun mistakes him for a homeless person while being very sweet and genuine, and tries to find him a nicer coat. When he eventually tells her he's a police officer she presumes he means that he's undercover and that she won't tell anybody. (Either that, or she thinks he's delusional and only believes he's a cop.)
In that same episode, Columbo pulls up to the scene of a crime, which happens to be a defunct auto shop. The officer on duty initially assumes that Columbo is there to get his car looked at and tells him the place is closed. Columbo identifies himself and the officer tells him where to find the man he's looking for. Columbo attempts to start the car to drive to the designated area, but it stalls out. He says, "I'll leave it here," and then leaves the car, unlocked and with the window rolled down, with the officer, who throws up his hands in exasperation.
In the episode "Mind Over Mayhem," Columbo is introduced talking to a school official, who informs him that he will have to withdraw his student. It turns out it's an obedience school and they're talking about Dog. Then when Columbo gets called on the case:
Columbo: "Could I just leave him here for a couple hours while I go to work?"
Official: "I'm afraid not. He depresses the other students."
In "Undercover," I laughed out loud at the fact that twice, while undercover as "Artie Stokes" and being sent to recover pieces of the puzzle mystery Irving Krutch has placed on him, Columbo approaches both Mo Weinberg and Geraldine Ferguson and both of them are fully convinced he's a cop, even when he says he isn't. The first scene with Geraldine is funnier because she's played by Shera Danese, Peter Falk's wife.
At the end of the episode An Exercise in Fatality, Columbo is rummaging around in his bag for the evidence that will prove the murderer guilty (while the murderer waits, fuming) and pulls out a squashed package:
Columbo: "Oh, that's my lunch; that don't mean nothing..."