Permission to view all private files

Not sure, if I got it correct but you can probably use public files instead of private. Public files will enable access to all files to everyone. To restrict it to just the authenticated users, you can capture the file callback and override it.

For e.g. if your files are stored in sites/all/files, than override it's callback whereby you can simply check if the user is logged in or not, using user_is_logged_in()

I had a similar case, fix it by using hook_file_entity_access

function hook_file_entity_access($op, $file, $account) {
  /* allow every logged in user to view all files */
  if ($op == 'view' && $account->uid) {
    return FILE_ENTITY_ACCESS_ALLOW;
  }
}

A patch to add a new permission "view any private files".

Updated patch with more consistent permission name.

Committed to 7.x-2.x.

@enochRoot not sure, it sounds like it might be an issue with the Media module.

we should add restrict access => TRUE here

http://drupalcode.org/project/file_entity.git/commit/d3a647f