Peter Arkadiavitch Stolypin, who was the Prime Minister of Russia from 1906-1911, mentions the Tercentenary in his meeting with Nicholas in Livadia. He is also present when the Tercentenary takes place. In reality, this would be an impossibility, as Stolypin was assassinated in 1911, and the Tercentenary takes place in 1913.
As Grand Duke Nicholas Nikolaevich discusses the family party to celebrate the birth of the Tsarevich Alexis, the tsar looks out a window at a scene of his daughters playing in the snow with Monsieur Gilliard, their French tutor. Alexis was born in August, so there would not have been snow, even in northern Russia.
In the ceremonial departure from Tsarskoe Selo on the way to the Dowager Empress Marie's birthday, when Nicholas and Alexandra stop at the door from the private quarters the court chamberlain is visible on the right side of the screen holding only his staff of office and wearing a plain black frock coat with gold lace. A minute later, as he precedes the imperial couple down the red carpet through the public spaces of the palace, he is carrying what appears to be a hat in his left hand (empty in the previous scene) and is wearing what appears to be the sash of the Order of St. Stanislaus.
In the final scene of the film, just before she is shot, Alexandra crosses herself from left to right in the Roman Catholic fashion rather than from right to left, the Russian Orthodox way, that she did correctly in all other scenes in which she made the Sign of the Cross.
The hairstyles the four girls wear when they are in the basement is based off the official photographs of 1914. In reality when the four grand duchesses were imprisoned they had their heads shaved due to illness. By the time they were killed in July of 1918 their hair had grown to the napes of their necks.
At the 1907 Fifth Party Congress in London, James Hazeldine's character introduces himself to Lenin for the first time using the name 'Stalin'. Not only had they met before, but the name 'Stalin' wasn't adopted until 1912.
In 1914, after World War I started, the city of St. Petersburg became known as Petrograd since the name St. Petersburg was considered too German. (It continued to be called Petrograd until 1924, when it became known as Leningrad.) However, in the movie, even after the war started, the city was still called St. Petersburg.
The 1918 wintertime scene where the family is exiled in a log cabin is wrong.
The royal family was exiled to a Governor's Mansion, not a cabin, when they were in the custody of Kerensky's Provisional Government, before the Bolsheviks took over.
The near-ending scene where the family is laughing about unflattering photos taken of them and reading letters from their relatives, friends and teachers has Nicholas saying "in a 'month or two'" as when "Mama" (Nicholas'; the Queen Mother) would be off to England in. Actually, Marie Feodorovna didn't go to England until 1919, the year after the family's July 1918 deaths.
Yurovsky is played by Alan Webb, who turned 65 in the year the film was released. In reality, Yakov Yurovski had recently turned 39 when he held the Romanovs in custody and participated in their execution.