Factual error: The film strongly implies that John Dudley, the Duke of Northumberland, keeps his head (literally) by converting to Catholicism. In fact, he was executed well before Lady Jane Grey was.
Factual error: In the scene where Lady Jane Grey is told she is now Queen of England, it shows her with her husband Lord Guilford Dudley, when in actuality he was not with her at the time. Also in that same scene, where they show her having the crown put on her head, did not actually happen until she was in the Tower of London.