it's not anger, but Columbo shows some annoyance when Paul Rifkin fails to give him the name of Jenifer Welles's other man at the jazz club. He says sarcastically, "Yeah, why would you ask for the name of the other man," and walks out,obviously disgusted.
In "Negative Reaction" during the final confrontation
with Paul Galesko (Dick Van Dyke) Columbo deliberatelyl gets hostile in order to rattle Galesko and to trip him up. What is interesting is that Columbo does NOT get upset when Galesko threatens him at the photo exhibition (I like it when he says to Columbo "you are like a little shaggy-haired terrier who has grabbed on to my trousers and won't let go" and "you are always looking at me with that fake innocent look"-Columbo maintains his calm in spite of this!).
The "A Stitch in Crime" and "An Exercis in Fatality" scenes were genuine anger. So was the movie set scene with Joan Hudson is "Prescription: Murder," though the Columbo character had not yet fully been developed.
However, getting "angry" with Ray Flemming in the final scene of the pilot was not genuine anger because Columbo knew that Joan Hudson was not really dead.
I've always thought he made a bit of a mistake in that "Exercise," scene apart from the anger, and that's that he accused Milo very directly, in front of witnesses. I don't know about these things, but if there were no arrest later on, could that be considered slander? As for being tempted to hit him, I doubt that "out of shape" Columbo (his own words) would hit a famous health expert, unless he were VERY angry. (Let alone one played by Robert Conrad, considering his tough guy image, on and off television!)
It took me the longest while to think of this, but one reason for his anger at Dr. Mayfield was that his original "victim" (the other doctor) was still alive, but "hanging in the balance." So for a change, Columbo wasn't just angry about something the other character HAD DONE, but about something else, that could be PREVENTED. So in a way, it was almost a one-of-a-kind scene for THAT reason too. Someone mentioned very mild cases of anger. In "Blueprint For Murder", Columbo goes from apologizing to Markham for those reporters (typical of him) to getting just a little mad when he finds out that Markham HIMSELF called the reporters (which is, of course, less typical).