Are you sure it's not because of your palms brushing the touchpad, causing the cursor to move/click? I catch myself doing it a few times... There's an option in the ALPS touchpad software that you can enable to prevent the cursor from moving whilst typing, which might help. Should be called 'touchcheck' or 'palmcheck' or something similar.
Downside to this is that it interferes with gaming (using keys + touchpad at the same time). Personally I just make sure to avoid accidentally touching the touchpad whilst typing!