Twitter doesn't do much but is extremely popular. Some of its philosophy could be extracted and reused for building communication-efficient tools.
I found three main ideas: conciseness, less noise and flexibility.
One could change the world with one hundred and forty characters. — Jack Dorsey
Very few characters are necessary to communicate about most of the things. Pick an amount depending on the task, the language and the craftmanship’s vocabulary. It can be 140 characters, it can be 300, but keep it short. Having less is best: it constraints your users’ verbosity. It help them to get to the point. How long does it take to read 140 characters? Maybe 10 seconds. Reading and understanding the point of an email can take more than 5 minutes. For lots of tasks, users can cope with a few characters, and maybe everything else they wanted to say is mundane and can be automated.
Only get updates on what (or who) you are interested in. This helps you to focus. It should be possible to poke you to get your attention, though.
Let your users find their own solutions. Only build features that are essential and forget about those which are not. This is what the 37signals folks call Human Solutions. If your users really need a feature, let them (or help them) find a way to work around it. Twitter’s tagging system is a good example. Originally there is no way to tag your messages. But use a special syntax—which becomes some kind of convention—in your message and you have a tag! Flexible systems are a win-win relationship: Advanced users are able to use complex features, whereas the system remains simple for the novice user, without requiring any extra development.