We use a combination of log formats in nginx and lmon to catch things like this. An NGINX log format like:
$connection $remote_addr $host $remote_user [$time_local] "$request"
"$http_referer" "$http_user_agent" "$http_x_forwarded_for"
$upstream_addr $upstream_cache_status "in: $http_cookie"
Will capture a lot of helpful diagnostic info, like the upstream server that handled the request, as well as putting the status in the front so it is easy to read even if the logs are scrolling by pretty fast.
We use LMON to watch these logs and then alert us (pagers/email) if it sees errors, like 500s, 503s, 400s, in the logs:
This can help you be alerted to an issue when its happening which is the easiest time to debug it.
The other thing you should probably consider if you haven't already. By default nginx considers a 500 to be a fatal condition and doesn't try another upstream. If you have multiple upstreams you can configure it to use another one if it gets a 500, hopefully obscuring the failure from the user: