It has exactly the same problem as blogs which is that to be blunt most people/blogs/feeds really aren't that interesting. You have to sift through the dross to find the handful of decent blogs or twitter feeds. This isn't a problem with the actual service behind it though. Just that there really is a lot of junk and its hard to find the decent stuff.

I can see some uses for Twitter but I'm not personally a fan of it. The artificial limitation to 140 characters just promotes the compression of messages into barely understandable gibberish. At least with SMS you generally have the ability to span multiple messages if you want to send a long message.