This is a result of word saving a file named ~$test.doc as a temp file, the server is rejecting the ‘~’ character, and this is from URLScan. URLScan can be configured to reject certain requests, including URI's with non ASCII characters in them. Please check if URLScan is installed and if so what its configuration settings are.

See the following MS article for details on URLScan.

Click Here To See Microsoft's Article Regarding URLScan

If you do not have URLScan installed, check and see if the filename contains any of the following characters: : / \ : * ? " < > | # { } % ~ & These characters are not allowed in SharePoint document libraries.