Word cannot save this document due to a naming or permissions error on the destination volume
This problem appears to be tied to how Word creates temp files when saving changes. The fix appears to be creating a .TemporaryItems directory with global read/write access at the root of the network share.

Creating a .TemporaryItems directory with global read/write access at the root of the network share should fix it. If a directory with that name already exists, check the permissions on the directory and set it to be globally read/write if needed.

Links with more information:

http://prowiki.isc-csg.upenn.edu/wiki/MS_Office_and_Network_Volumes
http://hints.macworld.com/article.php?story=20051122213207398