Simply change your functions accordingly:
private function addError($element, $error) {
$this->_errors[$element] = $error;
}
$this->addError($item1, 'required');
$this->addError($item2, 'required');
Of course this scheme will not allow you to track multiple errors for the same element at the same time; if you need to do that you have to rethink your desired result.