Being able to tweet “premium” or “public” tweets versus “private” or “personal” tweets would be a very useful Twitter feature. That way if you wanted to twitter your every thought, you could do it, but keep it out of your main stream of public tweets. Some blog services have Public/Private/Friends Only options. That would be very useful for Twitter. Friends could also perhaps choose whether to monitor your non-premium tweets, depending how close they really were to you, and how much they really cared about what you ate for breakfast/what toothpaste you used/how long your morning commute was/etc.

I see a split as something like this:

Premium
Tweets on interesting links, interesting photos, unique thoughts, original observations. The kind of stuff a normal person would take the time to write an interesting blog post about if they had more time.

Personal
Tweets on the minutiae of your daily life, your frustrations with minor things, a hi-score you just got in a game, a film or TV programme you just saw. The kind of stuff that is of little value or interest to anyone except the person it happened to, and possibly a couple of their friends or relatives.

This would also help professional twitterers who have work colleagues and clients and so forth reading their tweets. You can let people know about your products, your research, etc, and keep a more clean and professional Twitter profile/image by having your personal life tweets go to select personal friends. Currently one needs two accounts for this, which Twitter doesn’t make very easy.