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.
Continuity mistake: When Danilov first shows Vassili the leaflets that praise his exploits, the shot shows a leaflet coming off the printing press with four "x-ed out helmets", indicating how many German soldiers Vassili has killed. The camera follows the leaflet off the press, Danilov picks up the leaflet and hands it Vassili. The next shot shows Vassili looking at the leaflet, but now there are five x-ed out helmets.
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.
Continuity mistake: When Vassili is behind the chemical factory waiting for the Major to appear, the soldiers run out from under the train cars. The next shot shows the soldiers from behind, and if you look closely a horrible editing mistake was made. Some of the soldiers suddenly disappear, and then reappear.
Revealing mistake: When Danilov and Kruschev are in the war room, when they think Zaitsev is dead, pay attention to the maps on the walls. These are modern US and British defence maps that weren't available until starting about 1960. The clue is the the numbers on the squares. These are flight altitudes clearances for jets. Also, you can see that the maps are in Roman letters. Soviet maps during WWII were in Cyrillic and they looked differently.
Revealing mistake: Midway through the movie, there is a long-shot of several characters walking outside between two gutted factory buildings. The camera pulls back, zeros in on the base of a huge chimney and pans upward to the very top - where two men in black and white checkerboard jackets are working.
Continuity mistake: During the scene where Vassili is hiding from Major König behind an old oven and trying to get his gun back by tossing his pocket knife at it and pulling the string, König shoots the string. The string breaks, but the bullet doesn't hit anything behind the string, as if it was stopped by the string!
Continuity mistake: When Jude Law and Joseph Fiennes are walking through the Soviet Headquarters and talking about how the sniper never relocates, in the first scenes, Jude Law has no bandage on his wound on his head, however in the later close up shot there is a bandage, this within a few minutes. There definitely is no bandage present in the first scenes.
Continuity mistake: When Vassili and his two friends go out to trap König by shooting telephone repairmen, their rifles are covered by hessian, when they are shooting the repairman the guns are uncovered, and when Koulikov and Vassili are on the way back and jump across the gap in the buildings their rifles are covered again.