One of the biggest issues he mentioned was credibility. Tweets can be very anonymous, and their real-time nature leaves any information from them up in the air in terms of reliability. He mentioned that there are systems being developed right now to help offer more credibility, such as the ability to identify the physical location of where a Tweet was sent from. Another option being considered is a reputation system, given the people who read said Tweets an opportunity to rate their trustworthiness.
He didn't play the anonymous aspect of Twitter down. He said both anonymity and reliability are important, so finding a balance is their immediate goal. This is just speculation, but it could be that Twitter may delve into several different classes of Tweets -- some for people who prefer to remain anonymous, and some for those who want to be trusted at the expense of revealing more information about themselves. It's a short interview, but if you are interested in Twitter at all it's worth a read.