Software to run on server checking outdated wordpress installations

If you can access the files from the server just include wp-includes/version.php from each installation. That file is completely stand-alone, it just defines five variables:

/**
 * The WordPress version string
 *
 * @global string $wp_version
 */
$wp_version = '3.5.1';

/**
 * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.
 *
 * @global int $wp_db_version
 */
$wp_db_version = 22441;

/**
 * Holds the TinyMCE version
 *
 * @global string $tinymce_version
 */
$tinymce_version = '358-23224';

/**
 * Holds the required PHP version
 *
 * @global string $required_php_version
 */
$required_php_version = '5.2.4';

/**
 * Holds the required MySQL version
 *
 * @global string $required_mysql_version
 */
$required_mysql_version = '5.0';

A simple version_compare() will do the trick:

if ( '-1' == version_compare( $wp_version, '3.5.1' ) )
    return 'outdated';