By the time you push your code to production, it's hopefully robust, but you can't rule out unexpected errors. Thankfully, Django can capture errors and notify you accordingly.
Review your logging configuration before putting your website in production, and check that it works as expected as soon as you have received some traffic.
ADMINS
will be notified of 500 errors by email. MANAGERS
will be notified of 404 errors. IGNORABLE_404_URLS
can help filter out spurious reports.
Error reporting by email doesn't scale very well. Consider using an error monitoring system such as Sentry (for more information visit http://sentry.readthedocs.org/en/latest/) before your inbox is flooded by reports. Sentry can also aggregate logs.