In the final synagogue segment, while the congregation is singing "Aveenu Malchenu," they keep changing keys from shot to shot, up a half-step and down a half-step and back up again, indicating a string of takes edited together.
During Ryan Gosling's speech on Antisemitism his shirt color changes from gray to dark blue to gray again.
It's obvious that the Torah that's used in the film is paper. A real Torah is made of parchment.
A copy of The New York Times is shown with an article about Danny. However, the article is not printed in the font the Times uses.
In the DVD version, the words "a decade" are silent in the phrase "The Thousand-Year Reich barely lasted a decade..." even though Zampf is still mouthing it.