How do I enforce users to fill a determined custom field using WyPiekacz?

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. 🙂