Special Character Encoding Issues in Node Titles
I just checked with Drupal 7, and it will replace Unicode Character 'APOSTROPHE' with its NCR equivalent (&amp;#39;) in headings.  This is not a bug, but a security measure.

Apperently, when FaceBook receives this, it changes it to &amp;amp;#39, with the result you observe.  IMHO, this is a bug in how Facebook treats incoming NCRs, and has nothing to do with Drupal.  (It is not a good idea for Drupal to have plain apostrophes in headings.)  You may want to report this bug to Facebook, but it will probably not be their top priority.

You may also add a feature request to the authors of the module the sites uses to interact with FaceBook, asking it to rewrite NCR apostrophes into a single byte ASCII before sending to FaceBook.  They may be more symphatetic.

(Btw: This problem has already been mentioned on stackoverflow: https://stackoverflow.com/questions/11821400/apostrophes-turns-crazy-on-facebook-app - but I'm pretty sure the upvoted answer is hokum.)