Anachronic Order: Kyle Kallgren at Brows Held Highpoints out that this was probably done to stop the audience from noticing that the internal chronology of the film is both self-contradictory and flies in the face of almost all historical data.
A man appears in the beginning to admit that the story is just an intellectual exercise, not hard history.
The chronology is completely wrong. Macbeth is performed before Hamlet. Macbeth is widely considered to be a rather late production by Shakespeare, and directly references King James I (who ascends to the throne at the end of the film).
Also, Christopher Marlowe figures out that Edward is writing the plays, because he realises that the character of Polonius in Hamlet is meant to signify William Cecil. Shakespeare murders him to prevent the truth from getting out. Hamlet was first performed in 1601 (1598 in the film.) Marlowe died in 1593. You see the problem here?
The portrayal of Richard III as an Evil Cripple wasn't Shakespeare's invention: it appears as "fact" in Polydore Vergil's Anglica Historia, published in 1534 - over a decade before the births of both Edward and Shakespeare.
Cecil was actually against Elizabeth naming James of Scotland as her successor and for very good reason: it was Cecil, more than anyone else, who'd convinced Elizabeth to execute James's mother, Mary, Queen of Scots.
Beethoven Was an Alien Spy: William Shakespeare was actually a patsy for Edward De Vere, allowing him to publish poetry without affronting his aristocratic family.
Brick Joke: Ben Johnson complains that Essex's writing is just a passing hobby, saying "Last week it's gardening, now it's plays, next week it will be falconry!" Later, when Shakespeare is in Essex's study, there is a hooded falcon perched off to the side.
Coitus Interruptus: At one point, Shakespeare is interrupted while having sex with a prostitute.
Downer Ending: The fraudulent Shakespeare winds up taking credit for all of De Vere's work, De Vere is a failure as both a playwright and a human being, and Elizabeth dies without a legitimate heir, marking the end of the Tudor line.
Succession Crisis: With Queen Elizabeth old and having no legitimate children, the Cecils want James of Scotland to take the throne of England after her death. Edward wants it to go to the Earl of Essex.