It is stated that Filipp and the Tsar were childhood friends, but the Metropolitan was born in 1507, while Ivan the Great in 1530.
The events of the film happen between 1565 and 1568. Ivan IV, which was born in 1530 was 35-38 old in this period. Pyotr Mamonov, the actor playing this role, was 57-58 when he played it.
On 32nd minute a herald mentioned in his announcement current year as "1566" (according to Julian Calendar), although Julian calendar was introduced in Russia only in 1700 by Peter the Great. Gregorian calendar was introduced in 1918 after the Revolution.
In the beginning of the movie, commoners (muzhiks) bowing to the Tsar do not take off their hats, which is impossible according to the social norms of the time.