On a two person realm, when one person goes to the nether, the top half of doors near the portal (in the nether) appear in the overworld. (see image)

In my nether, there is a small room built around the portal. If two people are in the game, when one person goes through the portal, floating top halves of doors will appear in the overworld. This is frequent, but I haven't paid attention enough to tell if it always happens.

These doors seem to be "connected" to the ones in the nether. I pillared up to one of the floating doors and mined it. The similar top-half of the door disappeared for the other person in the nether. Opening and closing the door in the nether made the visual glitch revert to normal and the door didn't reappear in the over world.