One of the botched updates, KB3000061, from this month's Patch Tuesday offerings, fails to install. In fact, it will attempt to install, but then roll back after a reboot. It's been a couple weeks since Patch Tuesday and Microsoft is still working on a fix.
However, thanks to the community, at least one potential solution now exists, and the issue has been identified as a corrupted registry key.
The key: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\WINEVT
The solution has worked in a lot of situations, but not all, so don't take this as the ultimate fix without trying it on a test system first. Microsoft is still working on a permanent fix.
The full thread is here: KB3000061 fails to install on Server 2012