502 errors are usually caused when PHP freaks out for some reason. The first thing you should do is check all of your logfiles. That includes system stuff in /var/log/ and the nginx logs.
If you haven't made any recent changes and the problem just started happening for no apparent reason, PHP may be running out of memory. I know when it happens as an Apache module it gives a blank screen--wouldn't be surprised if a 502 error happened under nginx and the FastCGI interface. That's easy to fix by putting ini_set('memory_limit', '256M') into your index.php and see if that fixes the problem.
Also, can you load stand alone PHP files that don't involve Drupal? Put putting <?php phpinfo(); ?> into a file called info.php and try hitting that and see what happens.
Good luck!