When Vasily and Danilov arrive at the banquet with Nikita Khrushchev, the Soviet National Anthem can be heard playing in the background. This anthem was not adopted until early 1944, just over a year after that scene takes place.
The hand that Tania puts down Vassili's trousers has clear, shiny varnish on the nails. Possible in 1942, because it was invented by Michelle Ménard in the early 1920s, but unlikely to be used by a Russian soldier in Stalingrad.
Every pistol shown in the film seems to be correct, being either Tokarev TT-33's or 1895 Nagant revolvers, except for one. During the initial "human wave" charge, after the Soviet conscripts turn to retreat back to their lines and are cut down by friendly fire, there is one camera shot which shows two NKVD officers firing semiautomatic pistols. The nearest one is only partially visible, but appears to be a Makarov PM, rather than a Tokarev TT-33. The Makarov pistol was not designed until just after the war.
The locomotive hauling the troop train is a German "Kriegslok" ("war locomotive"). Captured Kriegsloks were not used by the Soviet Railways until after the war, and even then used mainly in the Baltic and border states.
The role which Eva Mattes is playing Mother Filipov. Filipov can not be a women's surname in Russia as all women surnames must end with an 'A' if her husband's surname end with 'OV', e.g. Filipov > Filipova, Maslikov > Maslikova.
In several of the scenes Jude Law's character is shown pulling hard on the trigger (or the rifle moves before the sound of the shot), this would have made shooting very inaccurate. People who shoot squeeze gentle on the trigger when firing, to minimize the movement of the hand and arm.
When Danilov is about to attempt to shoot the German officer, Vassily takes the rifle from Danilov, loads it, and sets the rear sight to 100m. Yet when Danilov takes aim again its rear sight is set back at the same place it was before.
In the scenes where the Russian soldiers charge out from under the train carriages, after Vassili falls asleep and Major König is making it across safely over the yellow heap, the charge is incoherent; The bunch of soldiers charging from under the train carriages have charged twice if you look closely.
When Commisar Davilov is showing Vassili the first leaflet with his story printed on it, he grabs a page fresh off the printing press, where you can clearly see there are only four helmet graphics shown with X's over them. In the close up shot of the same leaflet, there are now five helmets with X's, to signify the five Germans that Vassili killed. It appears as if the first prop leaflets designed only showed four kills.
After Vasily kills his first five Germans near the fountain, Danilov prints a leaflet extolling his feat of arms. When the leaflet comes off the press it clearly shows only four crossed-out helmets. By the time he hands the leaflet to Vasily a fifth helmet has appeared.
At about 46 minutes of the movie, Zaitsev comes back from the war zone. He has blood on his right forehead. Danilov starts to talk to him. Then all of sudden, a bandage appears on Zaitsev's forehead. Once they get inside of the house, all Zaitsev's blood has disappeared from his forehead, only the bandage is still there.
When Koulikov, Vassili and Volodya are going under the tunnel, Vassili spots a dead soldier. First scene shows the soldier with a grey finger. The second scene, after Vassili observes him with periscope, we see that the finger has turned red for a brief second, and after that scene we can see that he has no finger at all.
In the scene where Vassili first encounters Major König from the downed bomber outside the department store, after he fires he cycles the bolt on his rifle and a fully intact round is ejected, despite the round having been fired seconds beforehand.
When is shows Sasa in the German camp, he puts a boot on his cobblers bench to repair the sole, but it looks to be fine with no apparent wear. In the next shot the sole is heavily worn and Sasa precedes to replace it.
Vassilij is always called with his full name. That might be considered a minor goof, especially when such a name is used by the grandfather and Vassilij is a kid. A Russian grandfather is likely to call his grandson using diminutive like Vasja or Vasjachka (e.g. Tim or Timmy for Timothy).
The film often shows vast expanses of empty ruins within Stalingrad, particularly when Zaitsev and Konig are hunting one another. This would have been physically impossible at the Battle of Stalingrad, as hundreds of thousands, if not over a million solders were crammed into an area of only a few square miles.
Mass attacks such as the one depicted at the beginning of the film were never utilized in Stalingrad. Open squares such as the one depicted were few and far between, and all the actual fighting was done street-to-street, often with entire battles taking place in a single building.
The one ribbon that Major König wears on his ribbon bar is a non-combatant's version of a commemorative medal for WWI veterans. Not only is it unlikely that an ace WWII sniper would have been a non-combatant in WWI, König wears a combatant's WWI Iron Cross ribbon through the buttonhole of his tunic, directly contradicting the ribbon bar.
In the film, the troop train arrives near the Volga, so that the emerging soldiers can see the river and Stalingrad. At that time the rail line ended miles from the east bank of the Volga and they would have either marched, or ridden in carts or trucks to the city. (Cf. Walter S. Dunn Jr. Stalin's keys to victory. Stackpole Books, 2006.)
When looking at the German Sniper rifles you notice that the scope rings have screws in them to allow them to open and put the scopes in. This is incorrect. During that time, scope rings were a solid loop. The scope had to be dismantled and the tube of the scope slid into the rings, then the scope had to be put back together.
At the beginning of the movie, when map animation is shown, a very important fact is missed. The map looks like Soviet Union never invaded Poland on 17th of September 1939. Germany and Soviet Union cooperated together (which was mentioned later in the film by Kulikov) and on September 28th a new border was established. Part of Poland lost to Soviet Union was actually bigger than the part gained by Germany.
At the time of banquet honoring Vassili, the Russian anthem was the old "Internationale," which then became the party theme when the new (still familiar to some) Stalin-attributed theme of 1943 became adopted.
Danilov enthusiastically tells Zaitsev that their article will be republished all over the country, including in the Crimea, the Caucasus, and the Urals. However, the Crimean peninsula fell to the Germans in June 1942, before the film begins. This could, however, be an expression of Danilov's optimism that Crimea will soon be liberated.
The movie depicts events which occurred during one of the coldest and snowiest winters in Russian history yet we almost never see snow. The cold was so intense that it was considered a common enemy on both sides.
In the scene where Zaitsev is trying retrieve his rifle with a string and pocketknife, the German shoots the string, but the bolt on his rifle is not locked down. This would have resulted in a misfire and possibly would have injured the shooter.
In the scene where Vassili shoots the five soldiers, right after Danilov says "Don't shoot, don't shoot, he's looking right at us." You can see a foot moving amongst the dead bodies. The foot moving has a light brown sole, and Vassili's is much darker so it cannot be his foot.