When Brian Donlevy stops in alley to change his hat so not to be recognized. After changing his hat, the next shot (only a second later) shows that he also not wearing his turtle-neck sweater, but instead wearing a shirt and tie.
The pimple on Gestapo Chief Haas' face keeps moving around---in the opening scene it's above his left eye, later it's on his right chin, and near the end when he's looking at himself in the mirror as he squeezes it, the close-up shows it on his left cheek.
As the boy (Boda) picks the lock to open the door where Jan is tied up, he dumps the contents of his pockets on to the floor outside the room. Once he gets the door open he immediately goes inside and releases Jan. Once Jan is released, he and the boy rush out of the room but the things are no longer on the floor.
After the German soldier shoots open the study door at Czaka's house, the door is opened yet there are no bullet holes, around the door handle or in the door or frame, even though there were at least 10 rounds fired by a machine gun.
In reality, Heydrich was assassinated by a team of Czech exiles sent back to the country by the British government.
The character of Reinhard Heydrich wears the collar tabs of an SS-Gruppenfuehrer (group leader, roughly lieutenant general), three oak leaves. As Reichsprotektor of Bohemia and Moravia his rank was higher, SS-Obergruppenfuehrer (higher group leader, roughly full general). The proper insignia for this rank in 1942 was three oak leaves with a single pip underneath.
Heydrich was not shot. The gun provided to the assassins jammed. One of the men threw a bomb at the car that landed near the wheel and exploded, sending shrapnel through the seat and Heydrich's clothes before injuring his spleen, diaphragm & lung. He died from sepsis in the hospital days later.
When the German police disperse the crowd who've surrounded Ms. Novotny after the cab drove off, some of them start beating a young boy with wooden clubs. The clubs can be seen bending as they wield them.
When Ms. Novotny is being driven in the hansom cab to the Gestapo, there is a shot of the traffic in Prague with people driving on the left. When the Nazis took over in '39, they ordered everyone to drive on the right (as they did in Austria the year before).