New development: I tried updating my synaptics touchpad driver, but it required me to uninstall the previous version and restart. I did this, and
before I installed the new version (which I downloaded from Synaptic's website
here; the Windows 7 32-bit link for v14.0.3)
I noticed that I could get into the Mouse properties window, but couldn't change any settings for my touchpad, since it just had a generic Windows driver installed.
I installed the new driver (mentioned and linked to above) and voila the Mouse properties won't open any more.
I'm surprised there aren't more people who have experienced this problem if this is a compatibility issue.