One thing you can do is parse the tweets for mentions of certain words. In any event, you can alert people to the tweets rather than having them sit there. Not sure how large corporations handle it process-wise.
"ThinkUp is a free, open source web application that captures your posts, tweets, replies, retweets, friends, followers and links on social networks like Twitter and Facebook.
With ThinkUp, you can store your social activity in a database that you control, making it easy to search, sort, analyze, publish and display activity from your network. All you need is a web server that can run a PHP application"
Live demo:
http://expertlabs.aaas.org/thinkup01/index.php?u=whitehouse&...
http://thinkupapp.com/
"ThinkUp is a free, open source web application that captures your posts, tweets, replies, retweets, friends, followers and links on social networks like Twitter and Facebook.
With ThinkUp, you can store your social activity in a database that you control, making it easy to search, sort, analyze, publish and display activity from your network. All you need is a web server that can run a PHP application"