MACBOOK PRO Cursor Issues: Cursor keeps jumping all over the page

Are you sure you are not accidentally brushing the Trackpad with your palms? I find myself doing this on the later Macs which have the huge oversized Trackpads even when I'm paying attention and trying to avoid brushing the trackpad.

Does the cursor move when the laptop is just sitting there without typing? If so, then you either have a swollen battery which is pushing against the bottom of the Trackpad or you have a defective Trackpad. If you notice any bulging in the palmrest or trackpad or if the bottom case is starting to separate, then make sure you have a good backup followed immediately by powering off the laptop (a complete shutdown) and disconnecting the charger. Get the laptop serviced as soon as possible to minimize the damage caused by a swollen battery.

If you have "Tap to Click" enabled in Trackpad System Preferences is very easy to touch the trackpad while typing (I suspect that even just getting the hand close enough will trigger a tap but I'm not sure about that).

Finally there is an app in the MacOS app store "False Tap Stop" that rejects taps that occur while you are typing. This should solve this issue.