Here is how to invalidate dates in the past:
<?php
$form->addRule(
    'datefieldname', 'Date is in the past',
    'callback', 'classname::checkDateNotPast'
);


/**
 * Checks if the given date is in the past.
 *
 * @param array $arDate Key-value pair array with d, m and Y keys
 *
 * @return boolean True if all is ok, false if the date is in the past.
 */
public static function checkDateNotPast($arDate)
{
    $nDate = mktime(0, 0, 0, $arDate['m'], $arDate['d'], $arDate['Y']);
    if ($nDate < time()) {
        return false;
    }
    return true;
}//public static function checkDateNotPast()
?>

As this element is a subclass of HTML_QuickForm_group you can't use the addRule() method with the "required" validation rule, you must use the addGroupRule() method.

example:

$options = array(
'language' => 'en',
'format' => 'Ymd',
'minYear' => 2007,
'maxYear' => date('Y') + 2,
'addEmptyOption' => true
);
$form->addElement('date', 'TheDate', 'Date', $options);

$form->addGroupRule('TheDate', 'enter a date', 'required');