Bad Gateway means that php-fpm is returning an error to Nginx, so the trick is discovering what's going on in php-fpm. There might be more info in /var/log/php5-fpm.log (not 100% sure I have that filename right, it'll be close to that).
This might just be disguising an error that was always there, but resurfacing in a different way. Getting errors from Wordpress is a bit tricky since I don't believe it has a mechanism for capturing errors - so I'd check to ensure that php-fpm is setup to log a log file somewhere, and perhaps check php.ini directives to enable error reporting, increase memory limits, and perhaps check for it's own PHP log.
They key will be to discover, somewhere, somehow, an error message!
Bad Gateway may also occur if Nginx can't communicate to PHP, so double check to make sure there isn't an overflow of traffic to your server that you don't expect - something overloading the server?
Perhaps add the free tier of New Relic server monitoring to see if it spots any issues (full disk?)