Dominik,
Sorry for the delayed response.
On your page, there's another extension that's including the Facebook Javascript Library. If you open the HTML and search for "all.js", the second inclusion that has xfbml=1&id=xxx in it, needs to be removed. JFBConnect is also including that library in a way that is meant for more features to be used. I'm not sure if this is the exact cause of your problem, but definitely not helping the situation.
If you're still running into issues after that, we'd recommend trying the Facebook URL debugger tool. With that, you can see what Facebook 'sees' about the Open Graph settings for each page. From here, you may be able to diagnose why some pages act strangely:
developers.facebook.com/tools/debug/og/o...875-our-detox-decade
As for the z-index, we set the social buttons to a z-index of 100. That usually puts them on top of other contnet, but if there is a surrounding div with a lower z-index, they will take that index on and may make them go behind other content. If there's a specific place you're running into that issue, let us know the URL and button. We can look at the CSS and let you know if there's some code we can provide to help fix the problem.
Thanks,
Alex