Do we need to keep our hands on the Twitter brake in the classroom?

Using Twitter to extend the discussion outside of the classroom can be a double-edged sword (as can many other pedagogical techniques).  Yes, I do include Twitter as a teaching tool.  The question is how to gauge the use of Twitter so that is does support the discussion of in-class topics outside of the classroom walls.  Twitter can just as easily be a distraction as a help.  Several faculty have requested we look into some way to continue a conversation, topic, exchange of thoughts even after the class period is over.  I fully realize that faculty can easily overwhelm students with outside the class "activities."  We are always working with faculty to help them appreciate how much time it takes to participate in successful online forums.  However, Twitter might be a different type of animal.