What steps to take before an upgrade?
Also, are you using the Dashboard workflow to upgrade your sites or upgrading them manually? I prefer the manual upgrade process and feel like I have less issues with it (although many enjoy the in-app upgrade experience).
How to upgrade manually:
Only once you know exactly what steps are necessary (having learned on the clone), should you (take another complete backup) before upgrading the live site.
A slightly more complex variation is to make a staging site as a clone on the same server as the live site under a subdomain, upgrade the staging site, then once happy all is working, swap the domain name pointer, so the staging site becomes the live site.
The advantage the staging site and domain name swapping is that you can always swap the domain name pointer back again!
Another thing that is often useful is to swap to a default theme during the upgrade, then swap back to your real theme afterwards. That way you can't be locked out by any theme incompatibility that could arise.