I had a fresh look at the problem and noticed, that the parent directory '/var/spool/sa-exim/' were not owned by Debian-exim, but by me (a simple user). I believe that happened when I had to migrate the system to a new virtual machine. I now changed the ownership of '/var/spool/sa-exim/' to 'Debian-exim:Debian-exim' and I don't get this error message anymore.
I guess that resolved the problem and the bug report can be closed.
