Mysterious Door Opening
It was obvious, on inspection, that a draught had opened the door. The door touched the sides of the surrounding frame, without leaving any gap for air to flow around it, so that it jammed shut. This meant that air could not flow freely into the room, so obstructing the draught, which then opened the door. I repeated the experiment with the same result. Only when I closed it more firmly (firmer that apparently necessary) did the latch actually click, after which the door no longer opened.
So why was a draught trying so hard to enter the room? The obvious answer lay in a massive fireplace and chimney (unusually large compared to others in the building). The draught was caused by the Bernoulli principle (the one often mistakenly said to be the cause of lift in aircraft wings). The wind blowing over the chimney pots on the roof above caused the pressure to lower in the room below. This caused a pressure difference between the (effectively) 'sealed' room below and the rest of the building. Air pressure then opened the door. The pressure difference produced a draught once the door was open again.
If this incident had happened in a non-haunted location, I suspect people would simply put it down to draught (even if they did not understand the Bernoulli principle). It would not have been seen as paranormal at all. But, because it was in a haunted room, naturally it has become part of the 'phenomena' associated with room.