Anyone on Twitter can read your messages... including (and especially!) the people and companies about which you are tweeting! Hint: Thousands of users have keyword searches for themselves and their topics of interest. Believe me, they're watching.
Remember, even if you have protected your Twitter messages, someone else with an open Twitter account that you have allowed to read them may "retweet" (RT) your message and then it can be read by anyone.
Another consideration is that once you post anything to the Internet, including to Twitter and other social networking sites, you may as well accept that it is out there in ad infinitum... the "delete" feature of Twitter is far from being 100% effective.
Keep in mind that, unless you have blocked your posts so that only specific people that you approve of can see them, anyone in the very large and growing Twittersphere can see what you post! You never know who may be reading your messages -- your relatives, your friends, your coworkers, your customers, your enemies... or your future enemies if you are saying the wrong things in your messages!
If you are responsible for information security or privacy at your organization (or even in your home!), have you considered the potential uses and corresponding impacts of people participating in microblogs such as Twitter from your network? Now is the time to think about that and update your policies accordingly. Then, you should do some targeted training with those who are most likely to tweet, and also provide ongoing awareness communications about the related security and privacy issues.
Need assistance? I'm here to help guide and protect your company against negative exposure.
Thank you, and talk to you next month.
The Privacy Professor