I reinstalled everything, default Joomla comment settings using template modern, css black.
On a fresh Joomla there is no problem, on another Joomla installation only the editting acts buggy (both on the same localhost-server).
The original post does not get refreshed most of the times, and sometimes the editted post is inserted as a new post.
No javascript errors in firebug, so I don't know how to debug this. I hope someone else knows, or else I will have to make a component-page just for editting comments.