I have no idea why, but the AddThis dropdown doesn't show on my site after upgrading from 5.x-1.2 to 5.x-2.0-beta5. I'm only looking at a single (full) node. D5, PHP 5.2, MySQL 5.
Note what does happen when you mouse over the image: a long horizontal scrollbar appears and the vertical scrollbar gets longer. This indicates to me that the dropdown actually is appearing - it's just appearing very, very far away.