During the Kiev fight scene the amount of soldiers swap from shot to shot from a hug amount to a few soldiers.
The movie shows that Czar Vladimir I brought the Christianity to the people of the Rus. However Christianity already existed and was practiced before Vladimir's rule (during the years 978-1015), e.g. Princess Olga of Kiev (920-969), wife of Igor the Rurik, was one of the first Russian rulers who officially was a Christian.
A fighter mentioned that the Pechenegs started an alliance with Vladimir I of Kiev. However this didn't happen. They were fighting with the Byzantines and against the more dangerous Rus, mostly famous for the Russian-Pechenegs-Wars in the 10th centuries which were also won by the Rus.
It is mentioned that the marriage between Anna and the German Emperor, in this case Emperor Otto III of the Holy Roman Empire, was refused. But in real life she actually was promised. It was taken away from him by Czar Vladimir I of Kiev during the bloody fight for the Christian believe around Korsun'.
In the first fight scene of the movie, set in the 10th century, the Russians are fighting with Crossbows, which existed at that time but came to the region of Rus only in the 13th-14th century, mostly known from the source from 1376, while others say that it also existed in 1259.