Issue:
Trying to install Windows updates and update does not install.
Gives error code: 0x80073712
Fix:
1.
Run System Update Readiness tool.
checksur.exe
Download here
http://windows.microsoft.com/en-US/windows7/What-is-the-System-Update-Readiness-Tool
2.
Install Service pack 3 if not installed.
3.
Run System File Checker tool.
sfc /scannow
4.
If that does not fix the issue, it is recommended that you re-install Windows (meaning that Windows has a lot more issues than just the 0x80073712 error).
Read more at
http://support.microsoft.com/kb/957310