Once you destroy a door at its bottom, the top is briefly shown as open.
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is duplicated by 5
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Can confirm this for a split second (probably one tick / frame)
But this looks quite unfixable / working by design at the moment since the facing and the open/close state is stored in the bottom half of the door: http://minecraft.gamepedia.com/Data_value#Door
Maybe that behaviour will change in the future when the 4 bit data value is replaced by something better.
Found some other odd behavior with destroying the bottom half of doors:
place the door on a single block facing any direction but WEST
destroy the bottom half of the door and watch how the top part briefly teleports to the WEST.