Communication is Important
As Chris Brogan likes to say, “you have two ears and one mouth,” so use them in proportion. The following article has a few tips on how to listen on Twitter: http://www.twitip.com/listening-on-twitter/
I’d like to add that using Twitter search or a tool like Radian 6 you can readily track your name, company and sentiment. Consider using this to track happy and angry costumers so that you can respond in real-time accordingly.
How are you listening? What metrics are you considering?