Seanholt,
Device testing after an upgrade is typically specific to each environment
You should initially read the release notes to observe any announced change in behavior and test those. You would then test all of your client-facing applications to make sure that they work in varying circumstances, in general. You would then throw in tests for admin-facing features. It could easily take more time than the upgrade, so focus on all client applications at minimum should be the base starting point. If you have a lab, running many of those tests ahead of time on the build you want to upgrade to will help save time.
Maybe others have ideas of tests that they conduct, but again, it is only important to you if it corresponds to your environment.