How I Use It
I mostly use the Chrome app version of Tweet Deck - can manage multiple accounts and have freedom in sorting and organizing.
I have hosted live tweet discussions during significant events with my students. The state of the union addresses and presidential debates were great opportunities for students to engage in a dialogue with each other about what they were hearing/watching on the TV. This created a nice space develop a conversation before our in-class recap of the event.
Furthermore, this has become an important "discussion" tool for those students less inclined to share out during class.
The biggest drawback I have found is that students are inclined to use Twitter as a pseudo-public text messaging board. They are not accustomed to using Twitter as an information gathering tool (it's intended use). As such, there is friction with students who hear "Twitter" and find out that we are not going to be using it like they do in their free-time.
I think this is a fantastic tool for customized information gathering on virtually any topic. Although Twitter is laden with blowhards - of all varieties - it is also surprisingly chalk full of experts from various fields who have taken to Twitter as a way to engage the public, share links to useful information and drive discussion in the "now."
Teaching a media literacy class, I find Twitter to be invaluable. Especially in the cases were Twitter breaks a story before any conventional news outlet (Boston marathon bombing). I also find it particularly useful when the Twitter-verse is responsible spreading inaccurate information. Makes for a teachable moment.