How to Upgrade SQL Server 2008 R2 SP1 to SP3 ?

I have successfully installed Service Pack 3 on an SQL instance running with the SP1. No test, the install is directly on the production server. Well this is not a complex task and the topic has been already asking for other versions, but I'd like to be sure to not forget some steps and having feedback from experienced dba is always welcome.

 Here are the ateps:

• list all bugs that have been addressed in the Service Pack. ie:https://support.microsoft.com/en-us/kb/2509302
  
• Take a virtual machine backup and backup all the databases.
  
• Disable SQL Server agent.
  
• Apply the Sp.
  
• Restart server/instance if needed.
  
• Check for the Service Pack level of the SQL Instance.
  
• Check for all entries in SQL Server Error Log about the Service Pack update and ensure there are no errors written.
  
• Referring step N°1, check for eventuals bug issues.
  
• Enable SQL Server Agent.
  

From the client-side :

• Check for any compatibility problem between his software and the SP3.
  
• After the install, check for client connectivity between DB/software.
  

Is there any step you'll find pertinent to add/remove/modify to this ?