Twitter...ugh. Although I have an account from ages ago, I am not a fan of this sight. One wrong move and BAM! anything you have said is in front of millions of eyes. However, if controlled, I can see twitter as a useful tool if focused on educated groups and focused on the education topic.
Educators need to understand how to use social media so that both they and their students are not improperly and irresponsibly posting inappropriate information, or displaying an organization improperly.
If Twitter came out with a strictly classroom focused news feed, that can be streamlined for individual classrooms, I think it could become a healthy format for communication, although as a teacher, I always prefer to teach social skills and how to use accountable talk face to face.