Zenphoto is able to create the cache images but is not able to display them. The cache folder has rwxrwxrwx permissions, the subfolders (albums) it creates get rwxr-x--x permissions and the thumbnails it creates get rw-r----- permissions. With these permissions, Zenphoto is not able to access it's own created images. When manually change the permissions to rw-r--r--, Zenphoto is able to read and display the images. So is Zenphoto running under a different user which is not the owner of the cache images after it creates them by itself? (..sounds stupid, I know :-) ..but obviously it looks like that to me.
I removed (commented out) now the following lines from Zenphoto's "cacheImage()" function in functions-image.php script in order to keep the permissions of the created files to rw-r--r--
line 484: @chmod($newfile, FILE_MOD);
line 492: @chmod($newfile, FILE_MOD);
Hopefully you keep a note about your change as you will have to re-do it on any update. More info about permissions needed (basically what my colleague already said): http://www.zenphoto.org/news/permissions-for-zenphoto-files-and-folders