When you shoot an arrow at a wooden/iron door (Trapdoors are not affected by this) then open or close to door the arrow will float where the door was, as if the door was still there. Regardless of the game mode of the player the arrow will float. I feel as if it should drop as if it were on a block that was moved by a piston or broken by a player. Oddly enough, this only happens when the arrow are shot on the top half of the door. The arrows shot on the bottom half of the door fall, just like I thought they would. These same rules apply when arrows are shot from dispensers.