The reason that most of us are seeing "black crush" or ugly blockiness in dark areas in videos and photos is that these artifacts are present in the source material. Blocky patterns are a result of compression, and are most noticeable at the extreme ends of the dynamic range, where there is the least amount of detail. So if these compression artifacts are present in the source material, why do we not see it on other devices? It is because most other displays are properly calibrated to gradually gradate dark tones from dark gray to black. In other words, on a properly calibrated display, the color #000000 (black, or RGB 0,0,0) is virtually in distinguishable from #010101 (RGB 1,1,1). In fact, it is hard to tell a difference until #050505 (RGB 5,5,5). Therefore, most of the clipping that occurs as a result of compression artifacts is hidden. However, with the Note, #010101 is very much distinguishable from #000000. Dark tones are too bright, and we're able to see clearly until #010101. Instead of gradually moving to black, at #000000, it drops off a cliff. This is why we see such a dramatic different between the darkest grays and blacks, and why this black crush issue is so noticeable.
The side effect of having grays that are too bright is that when watching Blu-ray quality HD video, the dark areas look washed out, and the picture lacks "punch". High quality video that is properly encoded very rarely have pure blacks (to avoid clipping). As a result, dark scenes appear too bright on our phones.
The method to test is with a gamma test pattern, which I have attached. Download QuickPic from Market/Play (free). Go to Settings -> Viewer, and check the box for 32-bit render. Then, download the attached .png file, and view it in full screen in QuickPic. Make sure to do this in a DARK room!
Each box with a number has a corresponding RGB value. For example, the box with the number 1 is RGB 1,1,1, and so on. Load it on your Note and report back the smallest number that you are able to see. Also, does it gradually go to black, or does it just abruptly go to black without a smooth transition?
Last week, I went to two AT&T stores, and tested every display model with this method. Even with the bright store lights, it was possible to see box #1 on every phone. Repeated the test on an iPad 2, Galaxy Tab 10.1, and Skyrocket. The iPad was too dark, as the entire left side of the test picture is unreadable. On the Galaxy Tab, I could see box #7 or so. The Skyrocket showed a similar problem to the Note, as it seemed to abruptly transition to black. However, it was still a bit smoother than the Note, and box #4 was the smallest I could see.
Here's a picture of the test on my phone. The right side is the test image itself, so you can see how it is supposed to look like on your computer screen. Compare this with what you see on your phones.