WWII German "dogtags" didn't have the name of the soldier on them. Instead they listed the unit that they were in when the tag was issued, and a serial number.
(at around 49 mins) The bottle of sodium thiopental has the entire label printed in French, except for the words "sodium thiopental" themselves which are in English instead of the French "thiopental sodique".
(at around 8 mins) Cartridges do not fire their bullets when burned, as shown when the Stuka is on fire. They rupture, and their brass casings pop off. But nothing is launched like a bullet from a barrel would be.
(at around 6 mins) The antitank Stuka carried two 37mm cannon, not 20mm ones. Each cannon carried 6, 8, or 12 rounds, depending on the clip loaded into the weapon. These weapons were also rather slow firing (~160 rounds/minute). Thus, the cannon would not have fired as shown in the film - not at the rate shown, nor for the length of time.
(at around 7 mins) When Stuka plane crashes into the T-34 tank, there is a huge explosion, but the Stuka plane frame seems intact after the crash, just burning. Such impact would take place at some 300km/h, thus there would be just small scraps left from the plane.
(at around 7 mins) While a group of soldiers are walking down the road, two planes fly over head and the trees show no movement, proving that they are CGI.
When Grutas is having his chest shaved, he is accidentally nicked by the razor, yet there's no blood or mark on his chest.
(at around 39 mins) The French police are very unlikely to have used any polygraphs in the mid 1950s, particularly for 'normal' crimes like murder.
(at around 1h 4 mins) The trip from Lithuania to Paris, even by train, would take several days. Even without bathing or changing clothes, the smells from the forest would not be detectable.
(at around 1h 45 mins) The "village" of Melville is actually quite a distance from Saskatoon (at least 4 hours away). It is also not in the forest, but on the prairie.
(at around 1h 50 mins) The foliage shown around the village of Melville at the end of the movie is not found on the Saskatchewan prairie.
Mischa has always been a male name in Eastern European countries. It is the diminutive of Mikhail. A female name being remotely close would have been Mascha, a diminutive form of Maria.
If Hannibal had really been schooled in Japanese sword art, regardless of hand dominance, he'd have been holding the sword handle (tsuka) with his right hand on top and his left hand below. The Japanese always draw with their right hand.