Odd random rendering offset

I’m using the widget, in my sidebar.
I have FB Autoconnect Pro, and am using the large button.

When the page loads, the button renders in one of two positions, seemingly at random. One position is correct, the other is as if 10px of margin-top has been applied, and the button position is offset downwards – this is the majority behaviour.

I figured this might be due to a scripting clash, so I disabled all plugins and switched to the default 2012 theme. No extra custom code running at all. Same behaviour. The button renders correctly maybe one time in six. Same behaviour in all browsers (Mac).

I believe this has only begun happening recently, possibly since last update.

http://wordpress.org/extend/plugins/wp-fb-autoconnect/