Character mistake: A "Union Jack" on land is called a "Union Flag." Not so commonly known by the layperson, but certainly well known by the members of the British military.
Suggested correction: The Flag Institute, which advises the UK government and United Nations about British flags, investigated this idea thoroughly in 2013 and concluded "Union Jack" is perfectly acceptable whether on land or not. Union Jack and Union Flag have been used interchangeably in both Royal and governmental statements through the centuries. "It is often stated that the Union Flag should only be described as the Union Jack when flown in the bows of a warship, but this is a relatively recent idea. From early in its life the Admiralty itself frequently referred to the flag as the Union Jack, whatever its use, and in 1902 an Admiralty circular announced that Their Lordships had decided that either name could be used officially. In 1908, a government minister stated, in response to a parliamentary question, that "the Union Jack should be regarded as the National flag".
Factual error: When the Duke of Oxford (Ralph Fiennes) meets Rasputin, he notes how he "mastered the Bryozka glide", a dance technique where the practitioner looks like they are gliding a few cm over the floor instead of walking. However, while the scene is set in what must be 1916, the Bryozka glide was only invented in 1948 by Russian ballerina and choreographer Nadezhda Nadezhdina, who founded the Beryozka Dance Ensemble. (00:44:10)
Factual error: Conrad's rank badges as a second lieutenant are oval Garter Stars. This would be correct for the Grenadier Guards from 1919, but during the First World War the Guards regiments wore the standard British Army diamond-shaped Bath Stars (pips).
Factual error: The Black Watch sergeant major wears a crown over three chevrons, which was the correct rank badge for a company sergeant major until 1915. However, this is at least 1916 (as conscription has started and the men are wearing steel helmets, both introduced in 1916). CSMs had been redesignated as warrant officers in 1915 and now wore a crown on the lower sleeves instead.