Are you using Internet Explorer when experiencing this issue? Recent versions of Internet Explorer have a bug in XSS protection that in certain circumstances can cause apostrophe characters to cause issues.
However, the shortened link will not be shown on in the tweet dialog initiated by the Tweet button – the shortening happens once the tweet is submitted. The character count should indicate that the shared URL accounts for 20 characters if its an HTTP-based URL and 21 characters if its an HTTPS-based URL.
I do notice that you’re not “purely” using the Tweet Button here and are using an intermediary technology called AddThis – have you ruled out any issues the use of AddThis might have?