Since the initial error, due to an unrelated issue I ran sfc/scannow. After this, the installation continues farther, the progress bar goes all the way to the end, then regresses to about 50%. Finally it errors out with a completely cryptic message:
"Microsoft Office Professional Plus 2010 encountered an error during setup."
Again, the installation is to a Windows 7 Home Premium 64 bit system with Office 2007 Enterprise installed. I have read other posts where uninstalling Office 2997 and trying to install Office 2010 did not work and then were not able to re-install Office
2007 makes me leery to try to uninstall Office 2007.
I was having this issue on my user's machine and I was able to resolve it after capturing a Process Monitor trace.
It revealed that Network Service did not appropriate rights the HKCR\AppId Registry key.
Keep in mind that the Service runs in Network Service Account.
Added it, gave full access and it did the trick.