Forgive me my late arrival into the discussion.
I think I've said it years ago, the show really shouldn't even be called Arthur anymore... something more along the lines of Elwood City Kids or something, because when you think about it, the shift from focusing on just Arthur, and more on other kids actually dates way back to like Seasons Seven and Eight: we had a TON of episodes during those seasons where Arthur played no significant role in stories... that also seems to be around the time when there started to be more focus on D.W. and her friends, as well as expanding those characters... at least, it was the first time James had any significant role in an episode, and look at him now.
As for Nadine, I agree, she DOES serve a purpose, but only if she is utilized correctly, and that usually depends on the writer, and what the story is: there are times where Nadine can serve as something of a conscience for D.W., but then there are other times where she's just an imaginary friend.