There is a way for Luigi to eliminate a Fake Door, by simply sucking up a Fire Elemental Ghost and use it to burn a Fake Door. After that, the Fake Door will disappear. However, if Luigi enters two different rooms, including hallway corridors, the door will reappear. It should be noted that during the blackout, the number of Fake Doors have increased in more areas, as well as areas that had Fake Doors even before the blackout.
Using the Fire Element, you can also cause a glitch in the game. Where if the door vanishes as it's being burned and you press "A" quickly enough, an invisible door will flatten him. This is because the game doesn't expect you to do that and figures that the door is still there for that moment.
If the damage of a Fake Door causes a Game Over, the game won't have enough time to display Luigi's death animation, because the animation of Luigi being flattened and getting up again takes too long.
In Luigi's Mansion: Dark Moon, Fake Doors give Luigi the same fate as in the first game; slamming him against the wall multiple times. However, in this game Fake Doors will only make Luigi lose 5 HP. There is no way, save for the map, to tell a Fake Door apart from a real door, and since there is no Fire Elementals, there is no way to get rid of them either. On the map, they will not be shown, indicating that the door is fake.