I've had the same sort of experience. This is what I do to deal with it (it's part of my "install a new Ubuntu version recipe").
Create the /etc/X11/xorg.conf.d directory. In that directory create the file /etc/X11/xorg.conf.d/70-synaptics.conf with the following contents:
Identifier "touchpad catchall"
Option "PalmDetect" "1"
Option "PalmMinWidth" "5"
Option "EmulateTwoFingerMinZ" "5000"
Some also use a program that locks the touchpad for a couple of seconds each time a key is pressed--this is not an uncommon problem.
It's the options in the above stanza that do the trick. Your situation may vary because you have different hardware than me. Even if it works for you it may be necessary for you to adjust the values due to a different touchpad/keyboard geometry, different hand size, etc.