The whole point of Twitter is to know what's going on in the world of people and things you're interested in, BUT, and perhaps more importantly, IMHO foster conversation. The latter is completely opaque to someone who is new to the service. Conversation threads are buried under a click/touch and even then, it's hard to parse it.

I think the best thing Twitter could do is to downplay the importance of favorites and retweets (though they are important for growth but are a proxy for ego boost for the average user and not easy unless you're popular or important), and make the replies and conversations to a tweet/news story more prominent and "always-on" (with some limit of course, lest you see 500 replies to a Britney Spears tweet -- but then again, if you're following someone like that, may be you want to know what people are saying about it).

Engage more people in the conversation and surface it better. New users will have a much better grasp on what Twitter is if they do this.

My 2c.