In this lifehack.org article there are some good pointers for addressing random movement issues with your mouse cursor.
In my case the mouse moved randomly – both when using the trackpad and an attached mouse (USB, Bluetooth. In particular the “option-click” option wouldn’t work. Google searches were pretty useless, finding articles on how to set up “right-click” functionality for those coming from the Windoze World.
What I found was the battery had was starting to leak internally and had a slight bulge on it. This was causing it to press upwards underneath the trackpad, causing it to constantly “think” it was being clicked on. Removing the battery solved the issue (and probably saved me from an expensive service if it had leaked any further!).
Hope this helps someone out there!