The Event Viewer is always a must. I look at all the logs before and after the update to the domain controller looking for abnormal events. With the pre-check I usually go back a month of logs to get more historical data. I then run through a couple command line utilities. One thing I always do is pipe my commands out to a text document. This just makes it easier for me to read and also search for failed events.
Dcdiag.exe /v >> c:temppre_dcdiag.txt
This is a must and will always tell you if there is trouble with your DCs and/or services associated with it
Netdiag.exe /v >> c:temppre_Netdiag.txt
This will let me know if there are issues with the networking components on the DC. This along with the post test also is a quick easy way to ensure the patch I just installed is really installed (just check the top of the log)
Netsh dhcp show server >> c:temppre_dhcp.txt
Some may not do this but I”ve felt the pain of a DHCP server somehow not being authorized after a patch. This allows me verify the server count and names.
Repadmin /showreps >> c:temppre_rep_partners.txt
This shows all my replication and if it was successful or not. Just be aware that Global Catalogs will have more info here than a normal domain controller.
repadmin /replsum /errorsonly >> c:temppre_repadmin_err.txt
This is the one that always takes forever but will let you know who you are having issues replicating with.