When you are getting the following error - Error: Error: {faultcode:'sf:CONTENT_CUSTOM_DOWNLOAD_EXCEPTION', faultstring:'CONTENT_CUSTOM_DOWNLOAD_EXCEPTION: null', detail:{UnexpectedErrorFault:{exceptionCode:'CONTENT_CUSTOM_DOWNLOAD_EXCEPTION', exceptionMessage:, }, }, }, it's because you don't have permission to download the Files/attachments.
Check the Standard Download option to confirm your file download permission.
1. Go to the Account Tab and open any of the account records then click on the Notes & Attachments Section.
2. Select the file and click on the Drop-down then hit the Download button.
It will be throwing an insufficient Privileges error because you don't have permission to Download the Files. Here we confirmed download files permission is not assigned to your profile.
When you will get this permission, You won't see the error on Standard Download Button and Mass File Download app.