I have already modifyed my theme so that the text widgets get id="%1$s" class="widget %2$s". Now editing text-widgets works fine, if i turn on the WYSIWYG Editor. If i turn it off, the "ok"-button stops to work. "cancel"-button works fine, even with WYSIWYG Editor on.
I have no problem editing posts. This works with both WYSIWYG Editor on and off.
As i want to customize wordpress for a customer who doesnt want the WYSIWYG Editor in Front End Editor, this is a huge problem for me.