(Replying on this thread because it's about the bedroom door)
Well, Kate couldn't possibly know what position the door should have been in as Gerry had been in the apartment since she left at 8.30
She knew what position the door was in when she left the apartment at about 8.30pm.
She knew that GM and MO had been in the apartment since.
It was totally reasonable for her to assume that GM and MO during their checks either did not open the bedroom door, or that if they did they would certainly return the door to its almost closed position afterwards.
A 3 year old child is entirely capable of pulling a hinged internal door wider open.
Initially the child was in the north bedroom. Later the child wasn't in the north bedroom.
It seems quite obvious to me that the child pulled the door open wider to walk/run from the north bedroom into another room.
I think my chances of winning the "Most Complicated And Devious Moving Door Theory" award are small.