Besides grenades, the main weapon used by the Russian troops to blow up German tanks is an anti-tank rifle which blows up dozens of tanks. In reality, these were obsolete by 1942 because it could not penetrate a WW2 tank's armor.
The German Panzer-IV tanks all lack the turret machine gun which would have mounted parallel to the main barrel.
When the German BF-109 crashes into the Russian house, guide wires are clearly visible and one explosive at the point of impact goes off before the plane hits the ground.
During the first battle, a few of the Germans are carrying MP44 (or STG 44) assault rifles. This film takes place in summer 1942 and those rifles were not in service in the German army (even as prototypes) until over two years later.