Hi,
It’s funny – someone else reported this last week but it in fact had nothing to do with MapPress (it was caused by a javascript error in the theme). In that instance, addThis would appear intermittently if you kept refreshing the browser.
A quick way to find any conflicts is to switch to a standard theme like twentyeleven and deactivate ALL of your other plugins (except addThis and MapPress).
If that doesn’t help I’d be happy to look at it for you. Please describe more about what the problem is, and provide a URL for a demo page on your site, so I can trace it. On your demo URL please only leave those two plugins active and use twentyeleven.