2) Run the following command : "composite hello.png hello.png -compose difference out1.png" which will show the difference between the two files. In this case, they are the exact same file, so the difference should be nothing.
3) Display the file out1.png and it shows differences. How could a compare against the same file ever have differences?
Original Image (hello.png):

Difference Image (out1.png):

As a side note, we're seeing differences in separate files where we thought there should be none...that lead us to this sanity checking. This does not seem to be an issue when the images are jpegs.
Lastly, we did a Absolute Error count ("compare -metric AE hello.png hello.png null:" ) and the result is 0. So the compare tool seems to be telling us the right thing. Try downloading the hello.png image and running the composite command listed above. Perhaps there is something in the hello.png file that is confusing composite? Other PNGs and JPEGs do not produce this behaviour.
Let me know if more info is needed. Thanks.
Version: ImageMagick 6.6.1-0 2010-04-20 Q16 http://www.imagemagick.org (I have also seen this on the latest version of the windows binary)
OS : MacOs X (also windows)