I love that Jackie Cooper episode, too! The Nelson Hayward character in that episode seems to supremely represent two of the more contemptible things that many real-life politicians have been guilty of- unfaithfulness in marriage and being a hypocrite (Nelson campaigning against crime, yet being directly involved in it). I also love how his campaign manager, the victim, is a completely unlikable and revolting character, too.
I've only briefly seen parts of "Agenda For Murder", but I think I know who you're referring to- the guy who Patrick McGoohan's character is sort of in cahoots with. I agree that politicians make great adversaries, especially since they have so much to lose when Columbo catches them, so are naturally very contentious and defensive (sometimes to hilarious effect).