You beat me to it YM. I too, don't see Columbo's hounding of what's-her-name in "Prescription Murder" as arrogance. She was suspected of murder. Guess it depends on your definnition of arrogance. I don't see his outbursts in "Stich of Crime" or "Exercise in Fatality" as arrogant either.
I liked his "don't count on it ma'am" line in "Try and Catch Me". I saw it as a kind of gentle warning, even an apology that he had to do his job.

I was interested to hear how he stopped referring to his wife and started caling her Mrs Columbo. That is a subtle change and reminded me how much better it was when he did call her his wife.

Did Columbo get more arrogant as the series progressed? It's a good question. Perhaps, in accentuating the kooky side to his nature, in being a slightly more lighthearted (even at times whimsical)Columbo, he doesn't seem as earnest, as genuine, and appears slightly more arrogant, more self assured.
He bungs it on with his forgetfulness and whole schtick but now it seems even more contrived.

I guess he seemed to be more making fun of his suspects in the newer eps, patronising them more often with a wry smile and a wink to the audience that to me suggested a more arrogant Columbo.

I have no idea what Chief Clifford is referring to. I don't see arrogance to anywhere near the degree he described at all.

I actually like the scene with Kate Hudson in Prescription Murder. Miss Hudson is young, naive, and is being used by Dr. Fleming, but she also participated in a murder, and is covering for it. I think Columbo's outburst is justified and is an attempt to break the spell Dr. Fleming has over her; an attempt to appeal to her conscience, and the line "that woman would be alive if it weren't for you" is true, so I would say it's very justified. It's also a piece of superb acting which is enjoyable to watch!