If the mirror universe is defined purely by the orientation of the mirror rather than also its position. then simply moving the mirror towards or away from you disproves the theory.
ie. if you were looking into a parallel but flipped world you would expect the mirror to behave more like an empty picture frame than a mirror.
similarly if you move a mirror rapidly it pushes the air in front of it. If it was a doorway the air would move through it because the congruent air would be moving away from the surface.
If you try to get around this problem by saying that the mirror moves in the opposite way in the mirror world, then you no longer need to suppose a seperate universe per orientation of the mirror. The mirror becomes a camera in the mirror world and this same property explains 'flipping', mutiple mirrors etc. indeed this is how mirrors are modeled in computer games.