How to add validation to Drupal commerce checkout submit?
Drupal Commerce's checkout form uses button level validate and submit handlers as opposed to form level handlers. This means instead of just adding a handler to the $form['#validate'] or $form['submit'] array, you need to add it to the correct checkout button itself.

In your case, you'll add a handler to $form['buttons']['continue']['#validate'] via a form alter hook. Note that even if you prevent the form from advancing to the next page, though, that the checkout form is a special kind of form that validates and submits each fieldset independently of the form itself.

I'm not entirely sure how the registration module you're using interacts with the checkout form. However, it's possible what you may actually want is to alter the validate callback for a particular checkout pane via hook_commerce_checkout_pane_info_alter() to supply an alternate validate handler that checks your additional registration requirements and prevents that pane from submitting (which would also prevent the form from proceeding to the next page.