There are many settings that can cause the new document to get "broken" in sharepoint. I have gather the following list of corrections to solve this very annoying problem.
office protected view can cause issues
http://howtosharepoint.blogspot.com/2010/04/word-experienced-error-trying-to-open.html
Trusted Location OCT/GPO settings: (is 2007, about the same in 2010)
http://technet.microsoft.com/en-us/library/cc178948(office.12).aspx
Trusted Location Group Policy for Office 2010:
http://go.microsoft.com/fwlink/?LinkId=204009
print drivers, yes that can be the problem
http://blogs.msdn.com/b/askie/archive/2009/02/15/issue-when-attempting-to-save-documents-on-a-sharepoint-server-using-ie7.aspx
turn off sens with net stop command
http://blog.domcosgrove.com/this-file-cannot-be-saved-to-this-location-because-there-is-no-connection/
check ie settings as your security settings can break new document as well.
http://social.msdn.microsoft.com/Forums/en-US/sharepoint2010setup/thread/dde5c991-9164-4ca0-bbfc-ea72740d5335
on a server make sure that webdav is turned on, that is add desktop experience to your server. both 2007 and 2010
http://social.technet.microsoft.com/Forums/en-US/sharepointgeneral/thread/6f877870-aaa1-4ebf-bf03-560318b79487
and the list continues...
