The document "x" could not be saved. You don’t have permission
I was able to fix the problem for CleanWriterPro by removing extended ACL from the affected directories (Documents, Desktop):

$ chmod -R -N Desktop Documents


For others with the same problem, I'd suggest checking the permissions of at least the following places:


~/Library/Autosave Information
~/Library/Containers – see Unsaved Files in OS X Lion
the folders containing the problematic files


Use the command

$ ls -le Documents


to show also the extended ACLs when looking at the problem. Finder will not show all ACL information.

There is a related discussion at Apple Discussion Forums, Lion Permissions Problem. It proposes the solution of removing all ACL from home directory and restoring the ACLs for some default folders. Please read the entire post from there; but the commands are:

chmod -R -N ~
chmod +a "everyone deny delete" ~/ ~/Desktop ~/Documents ~/Downloads ~/Library ~/Movies ~/Music ~/Pictures ~/Public


The ACL prevents the user from deleting or renaming the default folders.

An unintuitive but maybe safer(?) alternative is described at OS X Daily: Repair user permissions in Mac OS X Lion