Despite the kinship of Elizabeth I and her cousin Mary, "Queen of Scots", the two of them never met face-to-face.
While pondering signing Mary, Queen of Scots' death warrant, Elizabeth says that Mary is her "father's sister's daughter". Historically, Mary was the daughter of James V of Scotland, who was the son of Henry VIII's sister Margaret Tudor. Therefore, Mary was actually Elizabeth's father's sister's granddaughter.
Elizabeth was not with Robert Dudley, Earl of Leicester, when he died. He had said his goodbyes to the Queen and headed for Buxton, and died en route. He had last seen the Queen one week prior.
When viewing a ship in the distance, the Earl of Leicester uses a telescope, approximately ten years before it was invented and certainly several decades before the first telescope arrived in England.
When preparing for the invasion of the Spanish Armada, one of the members of Elizabeth's Privy Council says that the Spanish will wish they'd never left Lisbon, which is the capital of Portugal. The Spanish Armada indeed departed from Lisbon historically. Philip II of Spain had also become King of Portugal in 1580, eight years prior, and many of the ships and crews that took part in the invasion were in fact Portuguese.