I was diving through the code for days but cannot solve this issue:
Because the provider of my server machine was changing the operating system, I have had to backup and restore the database and to change the directory of my wordpress installation.
To get it work again I have modified the database by hand: replacing all (hopefully) occurrences of the old path to the new path. Everything seems to work fine now ... BUT:
When I am in the "Write Post" | "Browse All" tab and choose an image I do not get the possibility "Show: Thumbnail" AND the preview is not a thumbnail, it is the full size image.
In "Manage" | "Uploads", choosing an image the problem does ot occur.
Additionally the problem does not occur for newly (after the restore) added images.