I am using the official Tweet Button from Twitter to allow users to share my site.
The button itself is working just fine, however the counter doesn't work and stays at zero all the time. (after you tweet, it is incremented client-side, but if you press F5, it will be zero again)
This is my really simple code to include the button:
<a href="http://twitter.com/share" class="twitter-share-button" data-url="http://www.whattheplace.com/Show/1/" data-count="vertical">Tweet</a>
<script type="text/javascript" src="http://platform.twitter.com/widgets.js"></script>
The specified URL (http://www.whattheplace.com/Show/1/) is a regular URL returning a web page with HTTP code 200, i.e. no redirection or the like that could maybe confuse Twitter.
I've prepared a small example on http://www.whattheplace.com/static/tweetbutton.html where you can see the problem. On the "real" page at http://www.whattheplace.com, the Tweet Button is wrapped by AddThis, but the problem is exactly the same.
I'm thinking that it might have something to do with the new Twitter URL shortener (t.co), however I can't prove it and it seems to work on other people's pages just fine.