this portion tells the tale:
[Wed May 09 19:48:19 2012] [error] [client 22.214.171.124] SoftException in Application.cpp:256: File "/home/lvmetrod/public_html/gallery/galleries/slideshow_dissolve/index.php" is writeable by group, referer: adm...oosedesign.php
it means the server does not allow the write attribute to be set for the group on that file.
using a dedicated FTP tool like FileZilla:
connect to your site FTP Server.right click on the /gallery/ folder and select "File Permissions"
set the permissions level to 755 and check the "Recurse into Subdirectories -> Apply to all files and Directories" option.