Factual error: At the end we see a soldier replacing the canister that the Zyklon B is kept in. However, he is not wearing an SS badge as all SS soldiers did. Zyklon B was only handled by members of the SS, as no other unit had authorisation to carry the sensitive stuff. (01:28:00)
Factual error: At the end, When the Jews are in the gas chamber, Zyklon B is dropped in through a vent at the top. While this is correct and represents the method used by the SS, the results are not. In the film it is depicted that the victims are dead within minutes. While this is true to a degree, the actual effects took 15-20 minutes to actually kill. Yes some of the more infirm people will have died quickly but the entire chamber would not have died that quickly.
Factual error: At the very start we see the Swastika flags hanging and they appear to be made of lightweight material. However, they were always made of heavier wool. (00:01:20)
Factual error: The senior SS officer visiting the commandant (and later at the funeral) is wearing two oak leaves and a pip on his collar patches. This rank badge didn't exist. Two oak leaves (without a pip) were worn by an Oberführer and three oak leaves with a pip by a Gruppenführer.
Answer: Samuel knew the dangers of the camp and knew that trying to escape would result in death. He knows Bruno is likely to be allowed IN to the camp as he is a German and Germans are running the camp. Plus, if Shmuel did escape, where would he go? He's 8, on his own and alone in the woods.