Factual error: The Bielski brothers go on a raid of a German post to acquire some "Ampicillin" to treat members of their refugee band who have typhus. Ampicillin is a penicillin derivative that wasn't available until the early 1960's, and in any case, typhus is properly treated with chloramphenicol or tetracycline, antibiotics of different classes from penicillin. Besides, the German didn't have penicillin of any type during World War II.
Continuity mistake: Midway through the movie, when Tuvia and Zus are fighting and the fight ends, Tuvia begins walking up a hill. As he climbs off Zus after the fight, the bottom of his jacket in the back is folded up. As he walks up the hill, the flap is down, but when he gets to the top of the hill and turns around to talk to Zus, the flap is folded back up.
Factual error: After the final battle, Zus dismounts the tank's machine gun and puts it over his shoulder, holding it by the barrel. But the gun has been fired throughout the preceding battle (which must have just ended, as the refugees are moving as quickly as possible and wouldn't hang around for more Germans to arrive) and the barrel would be much too hot to hold.
Continuity mistake: About 7 minutes into the movie, when Tuvia, Zus and all are meeting in the forest, there is a shot of Zus pouring something from a canteen or bottle onto his hand. There's a quick cut, then back to Zus, where not only is he not pouring anything on his hand, he's not even holding anything in his hand. There's not enough time for him to put the canteen down.