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."
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 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).