The foreign observers in the Russian Army wear white, blue, and red arm bands to symbolize they are on the Russian side. The white, blue, and red flag was only adopted by Russia during WW1. It was white, yellow, and black before WW1, the colors were changed because they resembled the colors of the Central Powers.
Crypted messages weren't used during the Russian-Turkish war. Messages were sent by telegraph or with a courier.
When Cossacks come to save Varya and D'Hevrais from Turkish troops, they whistle and brag with their weapon. Real-life Cossacks avoided that kind of showoff.
On Mizinov's map, Pleven is written as "Plevna", and the map is in color. First, on imported maps, Pleven was always written as "Pleven", and second, military maps were black and white with Russian words.
A soldier wakes up the others with a trumpet tune. In real Russian army, soldiers first woke up, then lined up, and only then the music "Zorka" was played by many musicians.
Viktor Bychkov's character speaks about the city of Murmansk. The film takes place in 1877. Murmansk, however, was not established until 1916.
When checking Lukan's tent, Kazanzaki tells that the experts had verified a Turkish document granting Lukan all authority he needs: the signature and the seal are authentic. First of all, such kind of experts didn't exist back then. Secondly, seals weren't used by the Turkish back then neither.