I've had this problem for weeks. A couple of ants crawled from my keyboard, I thought they were responsible. I removed the backcover, inspected and cleaned, no ants, but the problem continued. I went through all the posts I could find looking for an answer. I followed suggestions, bought a triwing screwdriver, removed the battery, disconnected and reconnected the trackpad to the motherboard, reset the PRAM, cleaned the trackpad, still the cursor moved around the screen with a mind of its own. I gave up and hooked a mouse to the USB. I went to system prefs, and in Universal Access checked 'ignore trackpad when mouse is connected'. I worked for a day or so with the mouse, constantly irritated the USB port was on the left and I'm right handed. I missed the convenience of my trackpad. I wondered how it was behaving now. I disconnected the mouse, and to my surprise, my perfectly reliable trackpad was back. I guess it didn't like being ignored:)
Oh you're behaving now I thought, but what happens if I shut you down and restart?
I did and It's still behaving. Yay!