As Jack is lying face-up, his head at the tailgate of the truck, he beholds the naked sky for the first time. The world is passing by - from top to bottom of the screen. This is exactly the opposite of how he would see it from his established perspective. This is no small error for arguably the most beautiful moment in the film.
The morning after "old Nick" hits Ma, Jack sees the bruises on her neck. Later, she has the idea to pretend Jack's got the fever, but she remarks it has to be that day because the power was cut. Therefore it is established that it only has passed one day, but her bruises are gone. You can't see either purple, blue, green, yellow, as the common stages of it.
When Ma and Jack visit room at the end of the film, Jack opens the left door of wardrobe first, then the right. When he closes the doors, he closes the left first, then the right. The right door does not close completely (they are coordinated doors). In the next scene (a wider shot), we see Jack looking around and the doors are closed completely. When the scene changes back to a close up, the right door is not closed completely again.
The police cars say Akron Police Department and cars have Ohio license plates, but just about every scene that's outdoors in a non-residential area has recognizable Toronto landmarks (e.g. Nathan Phillips Square, Apache Burger, Victoria Mills silos, Prince Edward [Bloor] Viaduct). Also, Akron has 15 buildings that are over 150 feet tall, but the view from the hospital window has about 30 skyscrapers.
When Ma and Jack are trapped in the shed "room", there is a lot of time where old nick is not there. There is a window "skylight" on the top of the shed. There are multiple items that they could have broken the window with, and multiple pieces of furniture, in which they could have used to stack and climb out of the shed. This window was big enough for both of them to crawl out of. Instead s Ma chooses a different, much more riskier option of escape.
When they last visit the room, the door seems half open from inside. Ma even asks Jack if he wants it closed. When they exit, the door is obviously out of position, as the police must have broken it open.