Count comments and not trackbacks or pings

You can disable the functionality in which WordPress counts both comments and trackbacks as comments in comments_popup_link() function. ^[1]

Place the following function in functions.php:

/*

     * Comments counting

     * Counting only comments and not trackbacks/pings.

*/

function comments_counting($counting) {

     if (!is_admin()) {

          global $id;

          $comments_by_type = &separate_comments(get_comments('status=approve&post_id=' . $id));

          return count($comments_by_type['comment']);

     } else {

          return $counting;

     }

}

add_filter('get_comments_number', 'comments_counting', 0);

WordPress Codex: Function Reference/comments popup link