Mary, Queen of Scots, was not originally part of the Babington Conspiracy. Walsingham, who wanted her executed, got one of the conspirators to act as a double agent, and entrap her.
El Escorial, the Spanish King's palace, is really London's Westminster Cathedral. Since it's a functioning church, the production team had to wait until the last evening confession was done, strip the interior of everything recognizably modern, shoot every scene during the night, then put everything back in place by morning mass.
Raleigh mentions to Queen Elizabeth that he has returned from Virginia. Jamestown, the first successful English Colony in Virginia was founded in 1607, four years after Queen Elizabeth's death.
The execution of Mary Stuart, Queen of Scots, is shown with a single, swift ax stroke. Historically, it took at least two strokes; the first hit Mary in the back of the head (reportedly prompting her to cry out, "Sweet Jesus") and the second severed all of her neck save some sinew, which the executioner then cut through by using the ax as a saw. Some reports say the execution required a third stroke.
Queen Elizabeth I: There's something you could do for me - something I have not known for a very long time. But it's not to be spoken of afterwards. It must be forgotten. But just for now, a kiss?
Queen Elizabeth I: I have a secret, my dear. I pretend there's a pane of glass between me and them. They can see me, but they cannot touch me. You should try it.