Hi Grey,
I suspect that it may be some kind of config or support file issue, rather than related to the particular web site. I tried a few more things, and it's now working. I'll outline what I tried in case it helps anyone else.
QuickCursor works fine on my MacBook Air, which has been running Mountain Lion for a while. I did an upgrade install from Lion to Mountain Lion on the laptop shortly after ML was released. QuickCursor was installed before that upgrade, and has continued to work fine on the MBA.
The Mac I was having trouble on is a recently purchased Mac mini, which was migrated from an older iMac that had been running Lion. QuickCursor worked fine in Lion on the iMac, but since migrating, it's been behaving as I described.
After reading your message, I first tried quitting QC, copying the plist file from the MBA to the mini, and relaunching QC, but there was no change in behavior. I also tried quitting, deleting the plist file from the mini, and relaunching, but that also made no difference.
Next, I tried deleting the application and plist file and reinstalling it from the App Store. That also did not change anything. (I installed the app from a different account, because we keep our regular accounts as non-admin on this Mac, and have a separate admin account, which is where I installed the app. On the laptop, for convenience, I've used my normal account as an admin account.) However it still made no change when I logged back into my account.
The last thing I tried was to change my user account to an admin user. In order to do that, I had to reboot the Mac. After logging back in as me as an admin, I was able to get QuickCursor to work successfully. One other thing that changed at the same time was that when I logged out of my account before changing it to admin, I had inadvertently not checked the option to restore windows when logging back in. So it was either changing to an admin user that got things to work, or it was resetting my window state.
I think it was more likely changing my user to admin, because I think I must have reset the window state at some other point between migrating to the mini and now, but I can't be sure.
After I got QC working, I logged out again and changed my user back to non-admin, rebooted again, then logged back in as me. QC continued to work, even though I was no longer an admin user.
So, beats me what happened to break it, but I'm glad I got it working!