Factual error: When Kruschev and Vasy go to the press meeting the Soviet National Anthem is playing in the background. The actual anthem was not written until January of 1944, a year after the Battle of Stalingrad. In addition, the song sung is the 1977 lyrics. The lyrics used in 1944 were slightly different. See http://www.skazka.no/anthems/ for more info.
Factual error: In one scene a Soviet T-34 tank is shown in the middle of the battlefield. This is clearly a T-34/85 model (as evidenced by the shape of its turret), which did not appear until late 1943. During Stalingrad, the Red Army was still using the older T-34/76 model, which had a smaller turret.
Factual error: Sasha reads a Russian newspaper account to König in which Vasily's new rifle is described as a "Mosin-Nagant." While this name is (and was) used in Western literature, it was not used to describe this rifle in Russia until long after the war; the gun was referred to simply as the Mosin rifle.
Factual error: Sometime in the movie somebody (I think the boy) says the Nagant rifle that Jude Law uses has a 4 times magnifying scope. When you compare the distance that objects have in the movie without scoping and through the scope of the rifle the magnification is way bigger than just four times. I know that cause I own a 4x scope myself.