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Although Leonardo Da Vinci died in 1519 and Thomas More's book "Utopia" was first published in 1516, Drew Barrymore's character is given the book as a present when she is a child and she meets the character of Leonardo 10 years later.
As depicted in the film, the real Leonardo Da Vinci kept the Mona Lisa with him all the time until his death.
Danielle's portrait, which Leonardo Da Vinci paints in the film, is actually modeled after another da Vinci work, "La Scapigliata" (also known as "Testa di fanciulla detta la scapigliata").
At one point Queen Marie tells Henry to choose a wife wisely, because "divorce is only something they do in England." This is obviously a reference to Henry VIII of England, who caused a huge scandal when he divorced Catherine of Aragon to marry Anne Boleyn in the early 16th century.
Mona Lisa is painted on a piece of wood and not on canvas as depicted in the film. This was done intentionally.