I'm no coding expert, but after spending the better part of a day fiddling with my site it seems that the latest version of WordPress plus the latest version of AddThis plugin plus Rockettheme's Syndicate theme (which has not been updated in quite awhile) result in the AddThis plugin not showing up on posts.
From what I can tell it has to do with the way the theme doesn't supper the new API Hooks formatting.
The way I fixed it was by downgrading the AddThis plugin back to 2.3.2. I've posted about it on the Rockettheme forum and am hoping they update their WordPress themes at some point soon to fix the issue.
Other 3rd party theme users experienced the same issue which was fixed once the theme developer updated their code. While downgrading the AddThis plugin solved the problem, it looks like it's not necessarily a problem with their code... but again that's not my bag.