For those looking to get control of the product order instead of using the random order or sorting by price or name I found this quick fix for the latest version. If, like me, you don't require the expiry date you can use it to control the display order of the products instead.
You just need to edit the "order by" section of catalog/includes/modules/featured.php to the below:
$featured_products_query = tep_db_query("select p.products_id, p.products_image, p.products_tax_class_id, s.status as specstat, s.specials_new_products_price, f.expires_date, p.products_price from " . TABLE_PRODUCTS . " p left join " . TABLE_SPECIALS . " s on p.products_id = s.products_id left join " . TABLE_FEATURED . " f on p.products_id = f.products_id where p.products_status = '1' and f.status = '1' order by f.expires_date ASC limit " . MAX_DISPLAY_FEATURED_PRODUCTS);
You can then order the products using an arbitrary date in ascending order.