The tweet widget doesn't show up at all when viewing my site in Internet Explorer 9. It works correctly in Firefox and Chrome.
There was a console error for the page that appeared to be related to the Google+1 widget. Removing the Google+1 widget made the error go away, but the tweet button still wasn't there. Looking at the page source, I saw only the anchor element for Twitter, and no iframe, div, img, etc., for the button.
For the time being at least, I switched to the general service link for Twitter and removed the tweet widget. But it'd be nice to have the tweet button work the same way as the Facebook, LinkedIn, and Pinterest buttons.