On my SP3:
1) I have similar problem in onenote2013, full-screen. When i write in that same spot, sometimes some lines disappear. Like an "M" would maybe look like an "N" or an "X" looks like an "y". Weird because im not lifting the pen, it just won't read the whole letter/line. (this happens mostly in the same spot as you on the video, but not necessarily, really annoying since I'm lefthanded)
2) I have also noticed that the pen is a bit off sometimes, which makes it nearly impossible to write, so i write on another place on the screen and theres no problem anymore.
On my SP2:
3) issue nr 2) was even worse on my SP2, but here it was in PowerPoint. I did a "hard" calibration of the pen - fixed!
It takes some time, you have to be accurate.
There is a post on the forum telling how to do it, i can't find it right now, will try again when I have the time. I think I'm gonna try this to resolve my issue with the SP3 as well. (I have already tried the normal version in control panel)
However I have noticed that my SP3 says im not connected to the pen via Bluetooth, which i don't get because it works in all other ways. Will maybe try to check that out first.
But.. I have to read for my exams first :/
Edit
Btw i downloaded the surface app from windows store, and put sensitivity to maximum which made things a _little_ bit better. This is the easiest thing to try out if it helps
Edit 2:
Omg...I have the exact same issue as you do, haf21. About the same spot on the screen.
I tried to make a video With my phone: