When the boy Ata is making a cross in the church he is doing this incorrectly. If he is Roman Catholic he should go from forehead to sternum to left shoulder then right shoulder. If he is Eastern orthodox he would have to go from forehead to navel then right shoulder then left shoulder. He does it from forehead to sternum to right shoulder ten left shoulder. This is not used in any form of christianity.
After having the panic attack, Jan was walking out of their room, past the family in the dining room. While Josef was putting on his coat, a camera man was visible beside him. Then Jan went on to give his carved statue to the old lady.
The opening text greatly oversimplifies the Munich crisis, and incorrectly states that Germany occupied the entire country of Czechoslovakia as a result. Germany never occupied all of Czechoslovakia, but only occupied the Czech lands of Bohemia-Moravia after having occupied the Sudetenland for approximately 7 months. Slovakia was allowed to retain nominal independence under a pro-fascist regime led by Slovak nationalist Jozef Tiso. The Czechoslovak government in exile placed great importance on showing that both Czechs and Slovaks rejected Nazism, which is why Josef Gabcik (played by Cillian Murphy) was made part of Operation Anthropoid.
At around 47:30 the character Josef Gabcík is shown shaving with a straight razor. He draws the blade at an angle of about 90 degrees to the skin. Just like with disposables, the blade of a straight razor needs to be held at about 30 degrees into the whiskers. What we're shown is a blade drawn at a right angle scraping the shaving cream off an already clean-shaven face.
When they first arrive in Czechoslovakia, Jan and Josef attend a New Year's party with Marie and Lenka. When they attempt to carry out their assassination plot four months later, they are all in light outerwear. While a warm day in April certainly is possible, the trees and shrubs in the background along the street are in full bloom -- well past what might be expected at the end of April in Prague. The European city at the same latitude as New York is Madrid. Prague is 10 degrees further north (approximately 700 miles). The trees should still be bare, as they are just starting to bloom in New York at the end of April.
When Jan and Josef arrive in Prague for the first time and exit their car, a satellite dish can be seen in the background on one of the houses in the street. This also happens when scenes are shot in this street later in the movie.