OK, after switching machines and updating to OS 10.5.8 on a G5 Dual PCIe machine, the ghost followed me there. Using the same keyboard and mouse, I decided to continue my internet search to see if I could find any clues. I found one forum where somebody claimed the microswitch in their mouse went bad. So I started to experiment. Remember that when I switched the left mouse functions to the right side, my problem disappeared? So I took apart one of those hokey cheap Chinese $4 mice and cannibalized it for a microswitch, which was (aside from the color), a perfect replacement part for my $20 Macally gaming mouse (left and right switches are exactly the same). Well, immediately my multiple click problem was gone. But I've given it a month before I returned to this forum. I am not saying this will solve everyone's problem here, but in my case it did. Also, what was interesting, was that the problem at times seemed intermittent. In other words, the microswitch was bad, but not always. This made it harder to pin down. But I see absolutely no sign whatsover of the issue now, and believe me, I'm happy about it. Also, I put that bad microswitch in the right button of the cheapie mouse. And guess what? Yep, that right button is set to clear the windows off my desktop, and just like the other mouse when I switched buttons, the windows fly back and forth multiple times. So this truly pins it down to the microswitch. Hopefully, you won't see me here again. Thanks to all, it helped speed up the process.
Yes, I think finally I have to admit that my mouse has died. I thought I'd tried other mice and got the same problem. Maybe I'd tried other mice, then after zapping the PRAM and trying other mice it worked - although that would make absolutely no logical sense.
Conclusion on my part = bad microswitch in mouse. ;,o(