Florian,
If you open the HTML of your home page, and search for "all.js", you'll see it come up twice. That file is the Facebook Javascript library, and it should only be on the page once. Please disable any other Facebook integration plugins, modules, or components you may have installed, and that should hopefully fix the problem. If not, let us know.
Just so you know, when the library is included twice, it will be completely browser dependent on if that issue would arise, depending on which of the all.js files loads first. That could explain why some users don't have issues and others do.
Keep us posted on how it goes, and good luck,
Alex