http://imageshack.us/a/img204/1671/galaxynotelongexposureb.jpg
This is a photo of an original Galaxy Note that shows exactly what all AMOLED screens have to a certain degree. Some phones have hardly any of this, some phones have a lot worse than this. This photo is the average.
The thing is this photo is not what your eyes will see 90% of the time. This photo was taken using a DSLR and using long exposure times to bring in extra light. This allows us to see in a digital photograph how there are black spots around the lit up panel. Because even with AMOLED, blacks still emit a very minor amount of light. Well, the black spots are pitch black, no light emission whatsoever.
I do not know what these black spots are or what they represent. Whether it is a manufacturing "defect" or just part of the natural organic substrate in a side effect, but whatever they are to those who own a device affected by it these spots are really really annoying.
Please, do not assume that "oh well my phone doesn't look anything like that photo" that you don't have them. Like I said, the light on that image is amplified many times greater than what it really should be to heighten the visibility of the spots. In reality the rest of the screen is nowhere near this "bright" and thus the spots blend much easier. Use this image as a guide to understand what to look for, the patterns etc, but don't assume they will appear so easily. You must be in the dark with your brightness all the way down and give your eyes 10 seconds to adjust before making a call.