Spurred on by some of the above attempts, I have finally fixed this by doing the following. I hope it works for others. You do need to get a copy of the kernel extension from a working mac however.
(1) Take a copy of AppleHIDMouse.kext from another mac running Mountain Lion 10.8.2 (in my case). I imagine that this could alternatively be another Mac running Lion 10.7.5 but have not tested this.
(2) Drag and drop copy this to /System/Library/Extensions/
(You'll need to authenticate at this point to allow finder to do the copy.)
(3) Open up a terminal window and change directory to /System/Library/Extensions/ using cd /System/Library/Extensions/
(4) Change the permissions and owner of AppleHIDMouse.kext via these terminal commands
sudo chmod -R AppleHIDMouse.kext
sudo chown -R root:wheel AppleHIDMouse.kext
(I acknowledge help from http://osxdaily.com/2012/01/12/how-to-manually-install-kernel-extensions-in-mac- os-x/ I did not need to remove the kernel extension caches spoken of in the above article)
(5) Reboot.
The Apple Wireless mouse then right-clicks and the correct system preferences graphic appears for the mouse.
🙂