I bought the first one probably around Jun 2012 and the second one end of August 2012.
I have 2 SGNotes (version 1) with black crushing problem. If you guys can confirm this is the defect from the screen, then I don't know if even a software/kernel fix can correct it because it is a hardware issue. These dark spots appear to arrange randomly on the screen and they look weird. Do this in a dark room and see if there are a lot of dark spots on the screen. In a related note about the screen problem with Samsung Galaxy Note (5.3' screen version), I also notice that if you have phone turn off completely, plug in the charger, briefly turn the phone on just so that it shows the green battery icon on the screen, then use your thumb or something to cover the battery icon, the rest of the screen will be illuminated by the back light from the battery icon. My only hope is someone comes up with a software fix at a lower level or a fix from Samsung, which is very unlikely provided their response so far.
I guess there is no hope of an easy fix for that problem. So, the 2x Battery app doesn't help in this case. Sorry, I was speaking too soon! Last night I tested a few movies while having 2x Battery app set my screen brightness/transparency at 80% and I saw a lot of blocking pixelations. Vbcomer, I have 2 SGNotes (version 1) with black crushing problem.