During the opening sequence at the Baltic Sea (November 1916, according to the captions), Admiral Kolchak identifies the pursuing German armored cruiser as the SMS Friedrich Carl and enters his own minefield in order to escape. Later, when the Germans are about to blast the immobile and damaged Russian vessel, they strike a mine and their ship blows apart and sinks within seconds with a clear big loss of lives. Actually, although the SMS Friedrich Carl was in fact sunk by Russian mines, this happened two years before than the movie shows (November 1914). Besides, she stayed afloat for several hours, enough for the light cruiser SMS Augsburg to arrive to the scene and rescue most of the crew, and only 8 crew members were lost. (In reference to a deliberate mistake, it is very unlikely that an experienced seaman and high rank officer such as Kolchak had mistaken a ship for one that the entire Russian navy knew had sunk two years before.)
At the initial battle, the naval tactics do not make any sense. In the movie, the Russian vessel remains relatively intact in its superstructure and hull, minus some fires, despite having received several direct hits, and the Russians are able to fire back and cripple the German ship. In reality, a cruiser like the Friedrich Karl wouldn't have to approach that close, and her 21 cm guns would have obliterated a Buinyi class destroyer like Kolckak's.
When Admiral Kolchak is addressing his troops in November 1918 at the Eastern Front, a variety of flags can be seen in the background, including an American flag that clearly has nine rows of stars. All American flags of this period had just six rows of stars; the US flag didn't contain more than six rows of stars until 1959, when on January 3 a seventh row was added to recognize Alaska's entry into the union, and on August 21 the stars were rearranged in nine rows in recognition of Hawaii's entry.
In Episode 5, the vehicle Kolchak is driving - in several scenes - has Texas license plates.