In the film, Robert Harley is a young man. In real life, he was 47-49 years old during this period. His youthful portrayal is probably inspired by William Pitt the Younger, who became Prime Minister at 24 in 1783.
In real life, Queen Anne didn't banish the Marlboroughs from England. John Churchill decided to leave England with his wife, Sarah, for several reasons: he had been removed from his role as head of the English army, he was facing bankruptcy (which meant he could not complete his palace Blenheim), and he was the target of personal attacks in the press and in Parliament due to several scandals.
Godolphin urges Queen Anne to send Marlborough an extra "division" to assist in the war. The concept of a military division and its usage as a phrase did not exist until about 30 years later, when the French general and military theorist Maurice de Saxe (1696-1750) invented it. De Saxe was a teenager during the events of this film.
The phrase "prime minister" was first used to describe George Villiers, 1st Duke of Buckingham (1592-1628), "favourite" of James I and Charles I. It did not mean what the modern office of Prime Minister has come to mean.
Emma Stone's freckles come and go. In the period depicted, an upper-class woman wouldn't spend enough time in the sun to acquire freckles. However, Abigail had fallen on hard times prior to attending court. Since she worked as a domestic servant, she could have been exposed to the sun long enough to develop freckles.
Mascara was invented in 1913.
An upper-class person is described as "posh." According to the Oxford English Dictionary, the first recorded use of the word in that context was in 1914.
Characters say "OK", an American expression first used more than 100 years later.
Multiple closeup shots clearly show second and third holes in Emma Stone and Rachel Weisz's ear lobes. Multiple ear piercings were not common in the early 1700s, especially for English women at court.
Wisteria in full bloom is seen..