Apple - My mac will not let me save word documents

The hint here is "... naming or permissions error on the destination volume." Word is telling you that it sees corruption/damage where you want to save the document.

And I'll bet you see it even if you try to save it to a USB key as well.

Microsoft is a great provider for those of us who do tech support for a living. What that error likely means is that something in MS Word (and possibly the rest of MS Office) on your system is damaged. The part is most likely in the part of Word that writes to disk.

What I would do is run the MS Word/Office installer and reinstall (or repair if that option is available) MS Word.

Failing that it could be that the temporary (recovery) file that Word creates for every document is damaged or that the preference file for MS Word is also damaged. The former is here:

 /Users/<username>/Library/Containers/com.microsoft.Word/Data/Library/Preferences/AutoRecovery.

The latter is here:

~/Library/Preferences/com.microsoft.Word.plist

Trash all the autorecovery files and trash the .plist file and launch MS Word again. That should fix it.

If not you may actually have file system damage on your HD. In that case boot into Recovery Mode, launch Disk Utility and repair/verify the disk.