https://www.tradingview.com/widget/ - Charts are great

as we all live a world market we need to be able to follow all markets around the world

Allow users to enter tweets directly on TweetTrader.net, so user don't have to use other Twitter clients to post messages.

Allow users to keep track of stocks (requires user account)

Show stock charts when you hover over the ticker when you hover over the ticker

Since this is made by a univeristy, its sience and it should be open and reviewable. and some people should be able to improve, comment, ...

What are you doing diffrent from those MIT guyes? http://arxiv.org/abs/1010.3003

would be cool to provide a api to tweettrader. maybe you can add a function to provide historic data too.
to start a rss feed would help the users too to be up2date - i think

TweetEveryTrade.com uses the broker's email notifications to automatically post trades as they happen or in daily/weekly summaries. It would be cool if TweetTrader.net integrated with this site or did something similar.

Have penny stock hot picks to micro hot picks. Not everyone is able to afford 30$ a share.

A ranking based only on the score is good if you make many votes. If based on percentage and you are lucky the first time... that's all. I suggest (even though a little technical) to use a ranking based on the binomial distribution: it is a good balance between number of votes and good predictions.

A comparison (graph or other) of your sentiment indicator over a long period with the stock or the index would be usefull to appreciate the accuracy of it...