In cases where the Windows 7 SP1 update fails, there may be a fairly easy resolution using a downloadable tool from Microsoft called the System Update Readiness tool. This tool checks the state of certain files and registry keys, and attempts to fix them if required. There are a certain set of errors (see table below) that this tool may help resolve when applying updates or service packs. These largely relate to Windows manifests and servicing components.
I updated my 3 home systems to Windows 7 SP1 today using Windows Update. On two of the three systems, the installation was flawless and fairly quick (for a service pack install). On the third, however, the install failed. When the failure was presented on the screen, I tried rebooting and running the update again. Once again, it failed. I checked into it further by clicking on View Update History in Windows Update, then double-clicking on one of the SP1 failed instances. In the Error details field it showed “Code 80073712”. Clicking on the “Get help with this error” brings up a Windows Help and Support article that references the System Update Readiness Tool. There isn’t much info presented on the tool, but it says that it may “correct some conditions” that cause this error. Unfortunately the tool is mentioned briefly in the Help article, then there is much more detail about repairing Windows. Definitely try the System Update Readiness Tool first. Thankfully a link is provided.