When you hover over the View Properties / Edit Properties links in the CSWP or the Search Result WP using these templates: https://github.com/SPCSR/DisplayTemplates/blob/master/Search%20Display%20Templates/Table%20Layout%20with%20Sorting%20Templates%20(CSWP)/SearchResultsWP/Item_List_Item.html
The links are incorrect.
The problem appears to be this line:
var viewPropUrl = String.format('/_layouts/15/listform.aspx?ListId={0}&ID={1}&ContentTypeID={2}&Source={3}', listID, listItemID, ContentTypeId, window.location.href.split('#')[0]);
It assumes all documents are in the same site as the Search site collection, which is not true in most cases. So the links do not work.