Mashable has an article, HOW TO: Use Twitter for Customer Service. It is really a step-by-step guide, but it does mention a couple of tools to use, Monitter and Tweetbeep. I would add TweetDeck to see direct messages and replies in the twitter live stream.
The article is correct that it is about being Engaged, Transparent and Authentic, as I wrote in my Social Media marketing 101 paper.
"Comcast, Dell, Southwest Airlines, Ford, Starbucks, and many more have been successful in promoting a positive brand image and solving customer problems with less cost than phone or email service. Twitter and social media are helping redefine how customer service is done."
If you are looking to see what some brands like Comcast is doing, read the Mashable article here.
One thing Mashable forgot, online and offline have to sync. [See here at PR Squared]. If your toll-free number doesn't help the customer but twitter does. Fix that! It costs approximately $30 per call and $1 per email. I would imagine that instant chat is probably about a $1 also. It's mainly labor, just like Other Social Media. Again, the offline customer service has to be in sync with the online effort. Or just be like Magic Jack. Don't give out a number for anyone to call. No email. Just chat. Anyway, have a strategy and go turn fans into fanatics!