Meyer states that Jonah appears in the Torah. The Book of Jonah is in the Tanakh or Hebrew Bible (known as the Old Testament by Christians), but is not in the Torah itself.
The small orchestra that greets new arrivals into the camps is factual, but the violin player would find it impossible to play his instrument with the bridge placed so close to his fingerboard and his bow on the wrong side of it.
Meyer Offerman's Auschwitz tattoo was on the wrong arm. The numbers were on the left arm, not the right.
When Johna is trying to get out the locked door of the shop, it's obvious the curtain on the door is covering a glass door, yet he doesn't think to try and smash the glass.
While the series is set in 1977, the game show Gretel Fischer watches in her Florida apartment is "Las Vegas Gambit", which did not actually premiere until October 1980.