Not that update errors ever happen, but MS has a new troubleshooting and fixing tool for borked updates, providing the update hasn't rendered the OS unusable...
"This guided walk-through provides steps to fix problems when installing updates. Here are some commonly seen error codes: 0x80073712, 0x800705B4, 0x80004005, 0x8024402F, 0x80070002, 0x80070643, 0x80070003, 0x8024200B, 0x80070422, 0x80070020. These steps should help with all errors and not just the ones listed." - MS
The tool works for W7, 8.1 and 10. And MS warns users that If you have W8, you should update to 8.1 as W8 is no longer supported. I'd take that warning seriously since the updates might well not be tested on W8 due to lack of support, and this tool will not work for W8.
The tool works in a stepwise fashion going through diagnostic, etc. algorithms but and if it cannot help, it will advise you to reset or reinstall your OS.
It's a good idea, therefore, to have restore points and updated backups for your system.
Download page for the tool: https://support.microsoft.com/en-us/help/10164/fix-windows-update-errors - you must choose your OS and then a download link will appear.