While I was playing on my world, I was standing at the exact area my door was in, but then, when I closed it, I was inside the door. However, I could easily walk out of the door. 

Steps to reproduce:

1. Walk directly into a door's hitbox.
2. Close the door while standing still.

Expected results:

You should be pushed out of the door, depending on which "side" you are on.

Observed results:

You no-clip through the door, and at certain angles, can't see the door in first person.

Notes:

I only have MCBE on my iPad, and this glitch is more conveniently performed in first person. Make sure when you look left or right, you see the open door. This glitch is best performed when the door is in front of your hitbox (if you stand behind it). Also, this works on almost any door (however, it is harder/impossible to do using iron doors). Update: I have now reproduced this with iron doors in the latest version.