Thanks for that Henry. It didn't do any of this a couple of months ago and using four different replacement mice (all of which worked perfectly before) didn't make any difference whatsoever to either group of symptoms. They each behaved in exactly the same way as the first mouse and as each other, even though they were each totally different. Does that still mean it's likely to be the "bounce", do you think?
Just to show my ignorance, do the wifi and cabled, the USB and the PS2 mice all share the same driver?