Where CO can make Twitter value add is creating an account that is not used for announcements but one that is used to explore complaints and issues.
A lot of people complain on Twitter:
http://twitter.com/#search?q=Continental%20airlines and it may be worth it to explore some of the complaints further and try to rectify the situations. Positive press and/or noise can't hurt.
If people are seeing "Continental Sucks!" and then "Wow, CO solved my issues", people may be less reluctant to fly them in the future.
Put an intern in there to monitor it and make a report of how many complaints are posted on Twitter every day/week/month and come up with a way to try and reduce that.