I start following @scoutapp. Because I'm following @scoutapp, it can send me direct messages. I tell Scout my twitter handle. Whenever Scout has an alert, you could send a direct message to my twitter handles with the alert summary and a shortened URL to the alert.
You've also allowed a bunch of hooks to occur via Twitter, for instance, I use Tweetie and I can have it Growl my alerts. It'd be a really sick way for my servers to communicate with me.