The revolver Daniel Craig obtained from the friendly farmer near the start of the film is a French army M1873 11mm-finding ammunition for it would be next to impossible by the time and in the place the film is set.
At the very beginning of the movie (around 40 seconds in), after the "Germany occupies Belarussia" information, there is a shot of a column vehicles entering the bridge. This is an excerpt from the Nazi war film chronicles ("UfA-Tonwoche") from September 1939. It shows Adolf Hitler's visit to the conquered Polish city of Gdynia, Poland's pre-WWII biggest military and merchant harbor. Specifically, it is the moment when Hitler's convertible car crosses overpass on the way to the harbor part of the city.
The object the Bielskis take from their house is a mezuzah, a piece of parchment (often contained in a decorative case). A mezuzah is affixed to the door-frame of Jewish homes to fulfill the mitzvah (Biblical commandment) to inscribe the words of the Shema "on the door-posts of your house". The parchment is inscribed with specified Hebrew verses from the Torah (Deuteronomy 6:4-9 and 11:13-21). These verses comprise the Jewish prayer "Shema Yisrael", beginning with the phrase: "Listen, Israel, the Lord is our God, the Lord is One."
The German tank which appears near the end of the film is a replica of a Panzer III which was created by modifying a Swiss Panzer 61 tank. It was one of two such vehicles previously used in Enemy at the Gates (2001).
An alternate opening scene would feature an old Tuvia, played by Daniel Craig in make-up, and his son in present-day New York City. The scene was filmed, but was cut by director Edward Zwick. The reason was becuase Zwick felt it would be "too nice" compared to the realism and brutality of the rest of the film.