First: Thanks for the great work :)
I installed wp-super-cache and (as far as I can tell) its working. I find the comment in the bottom of the pages, the cached pages are listed in the Cache Tester and I have no error (except the one, that mod_expires is not installed).
Also I find, that the homepage (index.php) is served super fast (tested using Firebug, Page Speed and YSlow), ~140ms compared to up to 1 sec before.
However, strangely for all subpages this speed boost does not apply. Actually there is not that big of a difference to before I installed wp-super-cache (~800ms). Even if the page barely has content.
Does this sounds familiar? Or must this be something outside of wp-super-cache?