Only button on the left displays the calender. The one on the right doesn't do anything at all. Also, for the records, I don't see any other errors like Javascript etc.
Vab,
Try replacing includes/templates/YOUR_TEMPLATE/templates/tpl_checkout_shipping_default.php with the one attached to my reply here (which will need to be unzipped, obviously)
Let me know if it fixes your problem and if so, i'll update the contribution.