I got some kind of error that Intellipoint needed to be reinstalled. Prior to that, I noticed that point64k.sys was coming up as "unsigned" when checking with sigverif. I'm not sure, but it might have to do with a November 2009 update to "Microsoft Hardware wireless mouse driver" or the mysterious "HID Non-User Input Data Filter (KB 911895)", which I can't find any info about. One last (but not least) culprit is the Thinkpad Ultranav pointing device that can have conflicts with Intellipoint & Microsoft mice. At any rate, it looked like the proper thing to do was reinstall Intellipoint and then do an overwrite install of the Ultranav driver and its "Utility".
Intellipoint has to be uninstalled before it can be reinstalled; the installer will refuse to continue if it detects that Intellipoint is already installed. I hope Microsoft changes this someday, because it makes fixing issues of corrupted installed much more difficult... especially when, as in my case, it did not show up in the Program and Features dialog box (previously known as Add/Remove Programs).
At first, I tried using autoruns (from SysInternals) to disable everything Intellipoint, then use Windows Installer Cleanup Utility (where it was listed), and some manual Registry editing to "uninstall" it. It was a disaster, but a System Restore made everything ok again.
Well, Intellipoint and Ultranav were both still messed up, and Intellipoint wasn't listed in the Control Panel as before. It didn't show up in Nirsoft MyUninstaller, either. At this point, though, I got a pretty good idea....
I forwent the Windows Installer Cleanup Utility. It might have worked, but what I did instead was extract the setup app, IPx64_1033_7.00.260.0.exe, using 7-Zip into a folder. Inside the extracted setup executable, I looked for the MSI file. I found ip.msi in the subdirectory ipoint\setup64. I right-clicked it and selected Uninstall. There was a UAC prompt, but there were no errors! I never got a dialog box that uninstallation was complete, but I compared with RegScanner, and Inteillipoint was indeed uninstalled! I rebooted, and I was able to reinstall Intellipoint (as well as the Ultranav stuff, subsequently) without difficulty. Windows Update automatically reapplied the "Microsoft Hardware wireless mouse driver", which is a little worrisome. However, everything seems to be working ok now.
All the tips/hints/fixes/other information posted here are at your own risk. Some of the steps here could result in damage to your computer. For example, using a Windows registry editor like RegEdit could result in unintended serious changes that may be difficult or impossible to reverse. Backups are always encouraged.