Where did the baby go? When Jacob is by the river with the baby you see her in the stroller. Then, as he's running away, the stroller is empty.
When the child and his mother are playing the piano, in the close-up shot of them playing the child's hand is on the left, when the camera zooms out the boy is sitting on the right.
When Bellamy and the kid Jacob are in a diner, Bellamy gives the kid his smartphone to play a game. Jacob starts playing and then stops the game to write something in another program/app. How does a kid who is dead and was away for 3 decades knows how to use that smartphone?