To be honest, this problem is really with URL shortening services rather than the plugin but it would be a lot easier to update the plugin than it would be to try and get t.co, bit.ly, etc fixed!
Basically, these services seem to make a complete mess of the URL if the anchor link contains characters like apostrophes. Better Anchor Links replaces the apostrophes with html codes but then bit.ly tries to remove those html codes!
The WordPress function sanitize_title_with_dashes is used by wordpress to create the to create a clean version of the article title for the article URL. Among other things, it removes ALL characters that aren't A-z/0-9 and replaces spaces with dashes. Could BAL be updated to just use this ready-made function? I've tried doing it myself by making changes to the mwm-aal-class.php file but I completely broke it as I didn't understand it properly. :)
Could the plugin creator or someone with more PHP knowledge than me please take a look at this?