Hi,
That's probably because there was a problem during the update process and the database structure wasn't updated correctly. So the query to add the product to the cart fails.
You should turn off the option "Use AJAX when possible for add to cart buttons" of the Checkout tab of the config and turn on the debug mode of the joomla configuration and try again. That should display an error message with the failed query. That will allow us to know what you need to do to fix the problem.
