I give up.
I've tried everything I can think of, to fix the behavior of the mouse cursor. I've zapped the pram, I've fixed file permissions, I've removed all startup items, I've tried starting the computer in Safe Mode. No can do.
The mouse cursor snaps back to a position on the screen when I try to move it. This happens within a second, so I might be able to move the cursor half-way across the screen, but that's it. It doesn't matter how fast I move the mouse. The cursor is dysfunctional in the normal user account, the administrator account and in the login screen. It works perfectly fine in Safe Mode.
The mouse cursor misbehaves when using a USB track-ball, the Magic Trackpad or the keyboard with accessibility settings.
After advise received at this site, I tried booting up in Safe Mode and after that the cursor worked for a month or so, but the problem returned. I see no rhyme or reason why the problem appeared for the first place, or why it reappeared. I had originally had two pointing devices the track-ball and the Trackpad connected to my Mac Pro at the same time. After the problem first appeared, I removed the Trackpad. I returned it to use a day before the problem reappeared, but I don't know if that is the cause of the problem. The computer had worked perfectly fine for some months with two pointing devices before the problem appeared.
I've noticed that some other people have had the same problem. One had a feline related fix, which doesn't help me since I don't have a cat. Another fixed the problem by switching off the Internet, but that didn't help me.
What I now would like is to make an official bug-report, so that the problem could be fixed someday. I hope Apple is listening. I also plan to reinstall Snow Leopard (I have 10.6.7) next weekend. I had hoped to install a new OS only when Lion got out, but I don't seem to have much choice not. I can either simply reinstall or make a clean reinstall by erasing the disk in the process. I'd like to avoid reinstalling my programs, but I feel it is safer to wipe everything and start from scratch. Even then, I have no assurance this doesn't happen again.