As I initiated this thread I wanted to give an update on my situation. I am not using the iPhone-app ever since I wrote this thread.
The syncing simply does not work any more.
A lot of praise goes to the stunning support of OmniFocus-Ninjas, that tried to help me a lot. I did not invest enough time to say, that their tips did not help. So part of the problem is me. :-D
Unfortunately my OmniFocus-File has grown to 20 MB although have hardly 1.000 Tasks. No wonder the sync does not work. I am using 4 different Macs, that sync regularly.
Does anybody know how to reduce the file size?