Some sketches I made a while ago to illustrate what I think a web-based twitter client could look like. I really like the Tweetdeck application, because it integrates lists in the most obvious way, showing all the posts like a dashboard. I think the basics of Tweetdeck could be very well made into a web-based dashboard.
What it would look like in your browser
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The entire page
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Photographs and other media links should be displayed inline. Like Twitstat does.
Reply and retweet should be inline as well.