Windows 10: "We couldn't complete the updates, undoing changes"

I've got the same issue and following on @Arthur's suggestion, I had a look at my user SIDs in the registry under HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\ProfileList and some of them belonged to users that no longer existed in the system (I had previously removed them).

I've removed the dummy entries (luckily there were only a couple) and the update worked.

PLEASE save yourself some trouble and backup the registry before trying that.

Fix for Windows 10

1. Go to Control Panel from Start Button
2. Go to System and Security
3. Go to Security and Maintenance
4. Click Troubleshooting in the Maintenace section
5. Under System and Security click the Fix problems with Windows Update
6. Let the troubleshooter run with administrative priviledges
7. You are done