After applying SUPEE 8788 on Magento CE 1.6.2, all customer can not login. My other problem is that is not possible to process an order on one page checkout. I saw few topic about the form-key, but I tried using magento default template and I have the same problem.
Any clue on that case?
That's because of missing form keys in the templates which you're using in your theme. You should update all phtml files from your custom theme by adding:
<?php echo $this->getBlockHtml('formkey'); ?>
immediately after <form ...> tag.
That's the only way.