I solved the problem, but it was a little more specific:
Sure, the JS caused the problem, but only because I administrate all plugins by dint of a self-made "Central Administration Tool", that deposits every plugin of any WordPress setup on my server in a central directory, connecting them with their specific WordPress setup via shortcut. (So I have to update a plugin used by two or more setups only once.) Using Contact Form 7 the ordinary way (without any Central Administration solution) it works perfect!
I don't think anyone else will have the same problem but... you never know. :)
Greetz,
lampi