sector0

I did some digging and found the answer on the Query Posts page, here:
http://codex.wordpress.org/Template_Tags/query_posts

By default, you can set sortorder to author, date, category, or title. There should be an array somewhere in the WP code that defines acceptible sort orders. If you can find that array, you should be able to add more (e.g. the modify date).

Here is an explanation from an older version. None of the instructions seem to work, but the concepts might still be true.
http://wiki.wordpress.org/?pagename=HowToChangeSortOrder

I put together a proof-of-concept template. It uses a form to pass the sorting details. Here is the relevant code:

<form method="get" name="testForm">
	<input type="hidden" name="order" />
	<ul>
		<li><a onClick="testForm.order.value='ASC';testForm.submit();">Ascending</a></li>
		<li><a onClick="testForm.order.value='DESC';testForm.submit();">Descending</a></li>
	</ul>
</form>
<?php
	if(isset($_GET['orderby']))
		$sortProperty = $_GET['orderby'];
	else
		$sortProperty = 'date';

	if(isset($_GET['order']))
		$sortDirection = $_GET['order'];
	else
		$sortDirection = 'DESC';

	$posts = query_posts($query_string . "&orderby=$sortProperty&order=$sortDirection&posts_per_page=-1&category_name=reviews");
?>