Due to a recent patch, the above code no longer works.
The following illustrates the necessary fix, which I've flagged with XXX:

function add_node_ids() {
  var trs = document.getElementsByTagName('tr');
  var i;
  for ( i = 0; i < trs.length; i++ ) {
    if ( trs[i].className == 'reply' ){
      var anch = trs[i].getElementsByTagName( 'a' );
      var id   = anch[0].name; // XXX
      var ntre = document.createElement('input');
      ntre.type = 'text';
      ntre.name = 'see_Free_Nodelet_Settings';
      ntre.value = "[id://" + id + "]";
      anch[0].parentNode.insertBefore( ntre, anch[0].nextSibling.nextS
+ibling );
    }
  }
}
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