I have no experience with this plugin. But when I look at the source, I think something like this should do it:
add_filter( 'wypiekacz_check_post', 'wpse_78395check' );
function wpse_78395check( $errors )
{
if ( empty ( $_POST['custom_field_name'] ) )
$errors[] = array (
'unique_error_key',
__( 'Custom error message', 'your_textdomain' )
);
return $errors;
}
Replace all strings in this example with something useful. 🙂