I think what you're describing is a 'rotated die' variety, where the obverse and reverse are not in the same orientation to each other. This can happen when one of the dies rotates slightly. Very small die rotations can be found, but really big swings in rotation are rare and quite collectible. These are easier to notice when you place the coin inside a cardborad coin holder (coin flip) with the obverse design oriented straight North-South. Then when you flip the holder over, the reverse should be along the same North South line. With a die rotation, instead it will be rotated (usually counter clockwise) by some degree. So yes, instead of 'pointing' at 12 o'clock, pointing at 11.
HH,
DirtFlipper