I'm finding this very tricky in a multi node environment, with code under revision control. AKA. multiple frontends and single database. I have a deployment process that pushes a git repo to the servers, but obviously if I update Wordpress from within the admin panel, it will update the files to one FE. Then I would need to copy over the new files to the other FE nodes. Plus, whenever these changes are written when Wordpress updates on a node, it writes code into the git repo. As such, it then breaks the auto deploys that perform 'git pulls', as it then has untracked changes and refuses to pull in new deploys unless manually intervened.
How does one easily keep Wordpress updated in a multi node (load balanced) environment?
I would suggest using a dedicated private admin instance and cron tasks to synchronize your service instances' filesystems periodically. You could use some kind of rsync process or an intermediate cloud storage service like Amazon S3 and sync tools like S3cmd.
I have successfully deployed some CMSs (including a Wordpress) in Amazon EC2 with autoscaling using the S3 based sync approach and, up to date , it's been working just great. I attach a example diagram of this setup.