I have obtained the Error with code: 80073712 yesterday while installing Service Pack 1 of Windows 7. I have no idea what was causing the problem, I have fixed it by installing the following update:
After installation of this pack, SP1 installed without problems.
Also I have run the System File Checker, which found some errors, repaired them, but also found some errors which he could not repair. So I don't know if it contributed to the fix of the problem.