Q: This PC will open. Doc documents (Word) as read-only purely arbitrary. I mean, this document will normally be opened on another PC and after closing the file on the PC, the other may or may not open as read only.

This is completely random (or so it seems). A document can be opened normally and the next is read only.
This has nothing to do with user permissions (we have a Windows 2003 domain server) .
This PC has this problem with users having this problem on other PCs ha