Mary is seen enjoying a late-morning cup of hot chocolate in bed (and even requesting it when she is a prisoner) despite this not being a popular drink in the British Isles until well into the 18th century.
The meetings between Queen Elizabeth I of England and Queen Mary Stuart of Scotland in the borderlands and in Mary's cell before her execution have no basis in any factual/historical account of these rulers. However, it is stated in the film that these meetings were secret and never mentioned even to Elizabeth's closest advisers.
At 1:11:50-ish, a man in the foreground is loudly ringing a large triangle with one hand, while holding onto the corner of it with the other hand. The ringing must have been looped in, because if you grip a triangle while ringing it, the sound is deadened and has no resonance.
Mary, Queen of Scots, wears small gold stud earrings throughout the film. They didn't exist in the 16th century, but were extremely popular in the 1970s.
When Mary returned to Scotland, she landed at the port of Leith, not on a beach.
James I of England (also known as James VI of Scotland) was born in Edinburgh Castle, not the Earl of Bothwell's estate. Mary was born at Linlithgow Palace.