During the scene where the woman is ringing the doorbell the little boy is in his pajamas. He is getting the dogs attention by blowing a dog whistle. Suddenly he runs outside and he has on a jacket coat and gloves. Then when he gets inside again he has on pajamas again.
This isn't a slip-up. The directors didn't want to waste precious film showing the viewers the obvious like putting on coats. First of all, Alex calls the dog from inside the coat closet. Now don't you think if he is smart enough to pull together this elaborate scheme that he is smart enough to grab his coat to go outside to get the dog? It is after all, winter! After he frees the dog and goes back inside, there is more than ample film time for Alex to be putting his coat away because the camera is on his mother. I think directors sometimes have to assume the audience has half a brain and will be able to make the connection so they don't have to waste film showing the obvious. Perhaps they assumed too much for some people in this case?