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.
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.