Now to classify what we mean as facing, let's assume it means the direction when you look straight through a door from the inner part. Meaning the direction it faces, matches the direction the face of the door is pointing at when first placed. This also means that the player must have been facing the opposite direction of what the door is facing. Now the table below shows how the texture of the non-moving part of the door changes when you open the door depending on the direction the door is facing for the front and side texture of the non-moving part of the door.

=Changes =Does not change
 

	North	East	South	West
Front
Side

One way to fix this is to add a side texture for the door and make that become the front when the door is opened and make the back texture become the side texture. I've also attached some images of the issue and some proposed texture of the side texture.