I don't want to presume to tell you how to use twitter but to me, it seems to be clearly geared as a one to many broadcast channel. It is much more akin to a protocol that allows people to subscribe to events/ideas/movements/news and get succinct updates about them. It is a terrible place for discussion objectively, but I believe this was by design-- and a feature.
I do agree with you there. Twitter is great for immediate notifications like that.
For discussion, if people, say, tweeted a link to their blog entry with their thoughts, I feel that would be a great use case of Twitter. Unfortunately some chose to do the entire discussion on Twitter. That often ends up poorly.
