Given his girth and venality, the character of Himmler seems to have been based more on Hermann Göring than Heinrich Himmler. Himmler had a rather slight build.
Heydrich had lost both his left eye and the use of one hand at the time of his assassination.
One character refers to Heydrich as the Protector of Czechoslovakia. There was no Czechoslovakia during WWII. Slovakia was split off into a separate country, administered by Fascist President Jozef Tiso. The Czech portion was renamed after the ancient territories of Bohemia and Moravia. Heydrich's title was Deputy Protector of Bohemia and Moravia.
In the cave, Jan Hanka picks up a Thompson sub-machine gun and asks how fast it fires. Karel Vavra tells him "about 300 a minute". Actually, that weapon fires 600 to 900 rounds per minute depending on the model.
Heydrich was ambushed in the city of Prague, not on a country road. His travel plans were also no secret: despite Hitler's admonitions Heydrich always took the same route when traveling in the city, believing the the people were too cowed to dare attack him.
A bus lists its destination as "Prague" A local bus would have used the Czech spelling of "Praha"
When Karel meets Jamilla's mother for the first time, there is a moving shadow of the boom microphone on the pillar above and behind them.