PHP to show if content has new comments in taxonomy-term.tpl.php? Is it possible to add some PHP to taxonomy-term.tpl.php that will look and see if any content tagged with the term has new comments, and if so print something in the html?
Yes you can but it will it performance without proper caching. Don't do that in tpl because you can cache it, even with page cache.
Code look something like that using drupal api.

&lt;?php
$has_comment = false;    
$nids taxonomy_select_nodes($term-&gt;tid);
foreach($nids as $nid){
$node = node_load();
  if($node-&gt;comment_count &gt; 0){
    $has_comment = true;
  }
}