Server Logs
Mostly, server logs typically replace the stream of information in the console.
You can set up logging here: https://docs.djangoproject.com/en/1.8/topics/logging/
Django exception email
With DEBUG
off, and settings.ADMINS
set, you will automatically receive a full traceback debug email every time there's an exception.
Runserver
You can also still run runserver
on production environments, then hit the URL via CURL or other to say drop into pdb
if it's an app issue.
Error monitoring tools
There are other tools, such as sentry
https://github.com/getsentry/sentry which is a joy to use and debug issues. It takes exceptions and sends them to a multi platform (even frontend/JS exceptions) exception monitoring tool and draws lots of useful exception data.
Newrelic is another application monitoring tool that would automatically track exceptions with full tracebacks.
Brute force
You can always write to files with only a few lines of python without relying on any major tools:
with open('some-file.txt', 'a') as f:
f.write('foobar\n')