I got notified that my blog was not accessible for a while. Seems that at least recent firefox versions somehow changed their behavior in what is send in the HTTP-header. This caused an Apache RedirectMatch rule to trigger, which denies access to some parts of the blog for some users.
The WP-login, WP-dashboard, and logged-in users where not affected by this, so if you have some custom rules which deny access to your blog, make sure you make a test of your blog when logged-out.