Hmm, that recording sounded mostly ok to me (I'm on my laptop atm however, so not the best thing to judge on). Really just seems to be the attack of the notes interacting between your pickups, fuzz and amp. Nothing to worry about too much imho. Are those active pickups? Also, different pick angles and depending where you actually pick in relation to the bridge/pickups can effect that type of attack a lot, as can the thickness/material of the pick.
While I do watch them, and still appreciate them, iPhone/shakey cam videos really get to me sometimes. Not because of the iPhone, but because of the audio and the shaking. The iPhone/iPad is actually not bad to record video on at all with good lighting. I used the iPad some in the Diamond pedals video I made. You've just really gotta cut over to amp-only audio when you go to play the guitar
So many hours spent in FCP automating audio.