Nothing too fancy other than following the recommended security practices. And to be aware of and regularly monitor the potential security holes of the servers/services I have open.
Even though semi-related, and commonly frowned upon by admins, I have unattended upgrades on my servers and my most of my services are auto-updated. If an update breaks a service, I guess its an opportunity to earn some more stripes.
All the legit reasons mentioned in the blog post seem to apply to badly behaved client software. Using a good and stable server OS avoids most of the negatives.
Unattended Upgrades on Debian for example will by default only apply security updates. I see no reason why this would harm stability more than running a potentially unpatched system.
Even though minimal, the risk of security patches introducing new changes to your software is still there as we all have different ideas on how/what correct software updates should look like.