Recently, Windows Update started failing for me on a few different computers, a few months apart. Site after site promised result after result, but led only to failure after failure. I accumulated a list of different recommendations, and what eventually worked for me: Using a VPN to avoid what seemed to be network-induced restrictions.
While the transition from my S4 to S6 has gone generally smoothly, I do miss the lack of support for the Xposed framework; specifically, the ability to create a wireless hotspot. However, there is a simple fix, with very little technical knowledge required (taken with gratitude from a post buried on xda-developers):