I found this issue in SharePoint Designer 2013 when accessing your SharePoint sites. It will pops up below message box repeatedly until I force to kill the SPDESIGN.EXE from the Task Manager. The message “The server could not complete your request. For more specific information, click the Details button.” is very vague and does NOT tell you what is the root of error.
When you click Details button, it does NOT any information as well.
It’s a simple solution if you know it. Enabling Anonymous Authentication for your SharePoint Web Application in IIS Manager will solve the issue. Microsoft site has further explanation on the issue and can be found here.