Open as temp sadly makes no difference. 
As a test I also tried to export the reports directly to pdf instead of opening them in the CrystalReportViewer control. This seems to work, so I guess it is a problem with the ViewerControl the framework provides.
If a try to view them I get the message from the very first entry of this post.
Strange thing is, that it is working when the js dialog for setting the parameters is used in the projects.
When such a project is loaded I can click on any other report and it also opens in the same instance of the CrystalReportViewer without errors.
But I need to open in correctly at the first time of course. 
Do you have any more suggestions?
Is there maybe a hotline which can help in such cases and maybe can look on my screen for a debugging session? I am out of ideas...