Hello breic,
Thanks for sharing this issue with the Community. I understand that your handwriting on your Surface Pro 3 looks erratic. I'll do what I can to help you with this issue.
In order to address this, we need some further information. We would like images which compare writing on your Pro 3 very slowly and at a more standard speed rather than the Pro 3 alongside the Pro. Also, could you verify that the writing looks worse when writing very slowly rather than very quickly. Is it that way, or is the other way around? Finally, have you installed all updates?
Please let us know so that we can help you further. Thanks again for posting in the Community.
Best Wishes,
Zack_T