Publish or Un publish any comment How to give moderator a right to publish or unpublish/edit any comment , not just own comment or  comment on own content without giving "Administer comments and comment settings" Permission, by giving just a tab for publish and unpublish for appropriate role ?
Go to /admin/people/permissions and check assign the appropriate permission("Administer comments and comment settings") you'd like to the that role.
Check https://www.drupal.org/node/777696