In general I don't find it all that funny. I think it's a kind of low-key humor, like the British The Office, that I don't exactly guffaw at. It's perhaps too close to true, not enough exaggeration? I am not sure.
But there was one little comment that stuck with me.
One of the pair - the Conchords is a duo from New Zealand (and I admit the jokes that keep confusing where they are from are pretty good) - mentioned in the intro piece that he is essentially a lazy person, and that "people like me oughtn't to be made to work so hard".
I like that. I relate to it, and I like that he took it away from himself, said that others should not make him work so hard.