I can imagine a world in which blog posts are filtered for interestingness. Filtering twits may not actually be possible. All text processing algorithms break down when you haven't got any text to feed them. I'd argue that it may not even be possible for another human to decide what's actually interesting to you, 140-char snippet by 140-char snippet, at which point you know a computer isn't going to do it anytime soon.
In fact, if you think you have a bright idea on this front to do a startup on, I'd challenge you to try the "human filter" first, and look at the accuracy you get. (Don't pick your clone; I'd suggest taking someone not entirely unlike you, but not your bestest buddy either.) If you can't even get that to work, forget it.
The idea is to integrate the libbow classifier with an open source twitter client. You vote tweets up and down, and future tweets will be scored based upon similarity to past good and bad tweets. Then, there's a slider in the settings panel that lets you select the percentage of tweets you want to see. The client will only show you the top N% of your tweets.
As the README says: "I have no idea what I'm doing in Objective C. This is a proof of concept for my personal use. Changes are super-welcome! Other Twitter client authors, please, please, please integrate this sort of functionality! I don't want to maintain this app; I want the good ideas to get adopted everywhere. Then this can die."
I'd love some help on the UI/Obj-C side, as well as a little more time to play with it.
I guess it depends on what you want to use Twitter for. I use it mostly to see what my friends are up to, and I don't follow people I don't actually know. News I can get from feeds (and I tend to be picky about those, too).
There is probably an opportunity here for a realtime "pagerank" for the various streams people use. If you think about it its a similar problem to the one google solved and look where that got them.
In fact, if you think you have a bright idea on this front to do a startup on, I'd challenge you to try the "human filter" first, and look at the accuracy you get. (Don't pick your clone; I'd suggest taking someone not entirely unlike you, but not your bestest buddy either.) If you can't even get that to work, forget it.