Florian,
Could you be more specific on how it’s “not working” in Firefox? When I select your links, they do indeed scroll through the page as expected. However, since your header element is dynamically calculating its height via JavaScript, this will create errors on the page as you scroll down. You will need to use a set height on the container above your navigation and remove the JavaScript automatically calculating the height of this section as that is what is causing the error I’m noticing in Firefox.
Thanks.