@mattyrob: Thank you! I misunderstood the feature (it was explained to me this way in the german wordpress forum).
@jameskoole: I am using the plugin “Subscribe to Comments Reloaded” now: http://wordpress.org/extend/plugins/subscribe-to-comments-reloaded/
It should be perfect for what you want. It even offers your users the possibility to follow comments without having to post a comment themselves.
JFYI: I solved the problem. I changed the code of the plugin such that it works with a FTP connection right now. So all folders and scripts have the same owner in the end, and this way the safe-mode conditions become obsolete.
sunny