As of October 1st Google’s Webmaster Tools will send out an email notifying you of any critical changes/issues that may impact your search listings, and your websites overall health – oh, as long as Google knows how to fix that said issue.
So, malware will be picked up, and a notification issued – but what else exactly will cause an email notification is uncertain yet – so I wouldn’t go ahead and cancel that Pingdom subscription just yet.
Either way you can control the amount of emails you get from within your email delivery settings.