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.
Revealing mistake: When the character played by Joseph Fiennes is in the Soviet headquarters, you can see his glasses shine with a purplish light. This is because his glasses are anti-reflex, something that was not available until much later than WWII.
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: When the car flips at the start, you can see that a ramp has been made especially for the stunt. (00:14:50)
Revealing mistake: At the start when the Russians are on the boat and being shot at via the planes, if you look really carefully you can see blood packs visible just as they get shot. (00:08:15)
Chosen answer: Vasily Zaitsev (Jude Law) uses a 7.62 x 54mm Mosin-Nagant M91/30 rifle with a PU scope. Major König (Ed Harris) used a 7.92 x57mm Mauser Karabiner 98 K with scope. Law's scope was wrong as the model used in the film wasn't available until after the Battle of Stalingrad.
Grumpy Scot