The Russian sniper is shot in the right upper arm after he lets the girl shoots the German. Later in the movie however, the sniper is not wounded.
When the Nazi soldiers are boarding up the windows of the bus with Rimma and her daughter inside, when seen from the exterior, the side of the bus is almost entirely boarded up, but when seen from the interior, there are only a couple boards on the windows.
When Kan pushes the curtains aside with his rifle to enter Masha's room, he pushes hard enough that it pulls the top left corner of the right curtain off of the rod. As Kan steps through, as seen from the other side, the curtain is back up on the rod.
When the Germans begin firing mortars, you see one of them drop a round down the tube, then place his hand over the muzzle for a moment. This is an unthinkable act for any soldier - as soon as the round reaches the firing pin at the bottom of the tube, it will fire, and any fingers over the muzzle will be on their way to the target. Any soldier with even basic mortar experience will know to keep his hand moving downward as soon as he lets go of the round. Firing a mortar is a pretty intense experience, and the muzzle is the most dangerous part of the weapon (for the person firing it), and it is just natural to keep your fingers away as much as possible. A soldier firing a mortar as depicted in the movie will only get a couple of rounds off before he runs out of hands.
The numbering of the German tanks is incorrect. For example, one tank has the number "716", which would make it the sixth tank in the first platoon in the seventh company. A German tank platoon had no more than five tanks, so it should actually end with "5".
Towards the beginning of the film, Ju-87 Stukas are shown attacking boats on the Volga, dropping bombs while they are in level flight. The Stuka was a dive-bomber - there is no way they could drop bombs that way and hope to have any kind of accuracy, certainly not on moving targets.
When Katya shoots the German getting water, the bolt (cocking knob at the rear) on the Mosin-Nagant is forward. It is essentially on Safe. When you cycle the bolt handle on the rifle, that part of the bolt stays back. It contains the firing pin. There is no way it can fire with the firing pin forward.
When Kan is driving through the crowd on the German Kettenkrad (the tracked motorcycle), he is just randomly twisting the left and right handgrips on the handlebars, which is doing nothing, as the machine is apparently being towed.
Captain Kan mentions how he had once been invited to meet Field Marshal Paulus. The problem is the movie takes place in November 1942 and Paulus was only a General at that time. Adolf Hitler didn't promote him to Field Marshal until January 1943, thinking that a Field Marshal would never surrender...He was quite wrong about that, Paulus surrendered to the Russians the very next day.
Of the model airplanes hanging from the ceiling, one appears to be a model of an F4U Corsair which was only released in 1942.
The German tanks have added armor plates of a type introduced after the actual battle of Stalingrad was over.
The broken down 'tank' in the German headquarters is actually a self propelled gun.
Kan should have known this when he asked when the 'tank' was going to be repaired. At the very least, the crew should have pointed out that it was a self propelled gun.