You missed the wp_nonce_field action name.
wp_nonce_field('submit-users-note''notes_nonce_field' );
$nonce = $_POST["notes_nonce_field"];
if ( ! isset($nonce) ! wp_verify_nonce( $nonce, 'submit-users-note' ) ) {
exit; // Get out of here, the nonce is rotten!
}