#2: Not listening for brand mentions and relevant conversations
Twitter effectively allows you to be the "fly on the wall" at a cocktail party. When an opportunity presents itself to join a conversation and interact, you should be ready. But you have to listen in order to do this efficiently.
Listening is a critical part of using Twitter if you want to be relevant and add value for the people who matter the most to your business. You can search Twitter as a lightweight form of brand and reputation management. Go to http://search.twitter.com/ to set up a number of persistent searches for your brand, as well as keywords that your users might be tweeting, and monitor them so you have the relevant knowledge of what is being said. This will allow you to respond and react accordingly in a timely fashion. You can also set up these searches as an RSS feed to monitor with something like Google Reader.