Rupert Mayer's father was also called Rupert, not Gustav, as stated in the movie.
In 1886 Rupert Mayer is portrayed having one sibling, a brother. In real life however he not only had his brother Egon but also had two sisters, Hermanna and Ines. Later two more sisters, Hildegard and Valeria were born.
In the scene set in 1920 the doctor said that Cardinal Faulhuber made Mayer president of the Marial congregation of men. However this happened in 1921.
The main building of the concentration camp Sachsenhausen in the movie looks nothing like the real Sachsenhausen.
In one scene set in 1937 a newsboy is announcing that Japan invaded China, which refers to the second Japanese-Chinese War, which began at 07th July 1937. In one of the following scenes Mayer is arrested during his sermon, which happened on the 5th June.
When military police arrives in Munich 1945 the American flag has 50 stars, not 48, as it should be in 1945.
Before the scene with Donna in her lawyer office a modern Bavarian flag is seen. It was introduced as an official flag in 1953. During the Nazi period the Nazi swastika flag should have been seen.
While it is true that the bells of Rupert Mayer's church in Weiler were taken by the Nazis to make bullets for the war it happened in 1942, not in 1937 as said in the movie before his second arrest.
In the scene set in 1937 Gabriel Goldberg is seeing wearing a Judenstern, the yellow star that Jews had to wear on command of the Nazis. However it was given out in 1938, one year later.
When Larissa is crossing herself in front of Mayer she touched first her right shoulder and the her left. This is how orthodox do the cross. For the Catholics it should be the other way around.