I am having this same exact problem here: http://www.bahairights.org
No matter what category I choose, I get this page: http://www.bahairights.org/category/
When i tried entering it without the widget with this code:
<li>
<h2>categories</h2>
<form action="<?php bloginfo('url'); ?>/" method="get">
<?php
$select = wp_dropdown_categories('show_option_none=Select Category&show_count=1&orderby=name&echo=0');
$select = preg_replace("#<select([^>]*)>#", "<select$1 onchange='return this.form.submit()'>", $select);
echo $select;
?>
<noscript><input type="submit" value="View" /></noscript>
</form>
</li>
I still got the same result.
When I change the permalinks to the default, the dropdown works. This widget works on other sites without any problems. Can anyone help?