It's really simple. I want my contacts organized in groups, just like any RSS client. When I open up my Twitter client, I want to go directly to my friends' new tweets before reading my celebrity or news tweets. I care more about jagosaurus or sgazzetti are up to than what celebrities like Wil Wheaton or Penn Jillette or John Hodgman are doing. And I want an unread count for each group, like most RSS readers give. The total unread count should be shown in the dock icon. Also: Link Unwrapping. I want everything that Tweetree does. All shortened urls should be unwrapped, the url and title of the page linked to should be shown. Links to twitpic, Flickr, YouTube, Blip.fm, etc. should have a thumbnail, and perhaps the audio or video, embedded in my tweet list. As I mentioned, Tweetree does all of this more or less perfectly. They also do tweet threading, but that's not a feature I care much about...not to mention that it's not really possible to do properly given the current Twitter API.
This doesn't seem that difficult.
Currently my favorite twitter client is Twirl, which doesn't do any of these things, but I've tried about a dozen. C'mon, developers! Make my dreams come true!