Is the problem that it is pressure IN-sensitive or that your strokes are interpreted as random/other strokes ?

I'm actually unsure. The problem was that whenever I put the pen against the tablet, the lines would ping off in random directions. No idea what caused it. There is tons of evidence pointing to the computer, the software, and the tablet, but it was unclear. The issue seems to have fixed itself though, so I can't say for sure what it was.

Hmm.. I myself had problems after initial driver installation after which the pressure sinsitivity worked as expected in Krita. But next day I turned the PC on I realized there were no pressure sensitivty at all. Tried starting the wacom driver settings apps. The wacom desktop app just crashed. The tablet (and pen) settings app couldn't start because the driver couldn't be found. I googled and went through a second page with question and suggestions. What worked so far was to disable a (windows built-in ?) service called Tablet PC Input Service after which the pressure sensitivity has been working as expected.
The topic starter in that page seemed to have had the issue magically go away without him/her (knowingly) doing anything.

A few times I have had the occasional random stroke going a direction (and length) totally different to mine, and I hope I do not experience many of those. Few days ago I saw a video in youtube where someone illustrated that (constant and regular) behavior on his Intuos Draw/Art/whatever and wondered what was wrong. He was sugested to uninstall driver and all Wacom software, then install newest driver, which seemed to have worked for him.

Ahhh... the joys of glitchy tablets; Im all to well accustomed to glitchy tech like this. With me my main tablet glitches ever so slightly once in awhile and wont work at all with PS while on my tablet\laptop (its like a surface pro) it gets random dots but still manageable. tried and Switched to PS on the tablet too and its working quite well... if you get used to the program not picking up pen movements occasionally. xD im a unlucky duck. heh

Oof, I feel ya pain .3.
Turns out the laptop was pretty wonky. Maybe more like "r e a l l y" wonky, actually. Then again, I was having a bit of the bad luck myself, using unregistered CSP. Moving to FireAlpaca was a real good decision. Less confusing, more stable, and best of all: I could actually flicking save my work X(
Hope whatever you've got going on manages to get resolved. I know from experience it can be a bit annoying.