Continuity mistake: Halfway into the film, Shakespeare is holding Viola's face placing his hands around her jaw, looking closely at her. When the angle is behind Viola, we see that her hair gets caught around his left hand's fingers. The angle changes to a wider side angle and his hand has no hair around, even though he hasn't moved it at all.
Factual error: About 20 minutes in when they are at some ball/dance thing, Shakespeare's talking with a musician holding a lute. You can see fret markers on the fretboard of his lute, but these were not used on instruments until the late 1800's, early 1900's, definitely not in Shakespeare's time.
Trivia: The young boy in the film is John Webster. Webster himself became a famous playwright in the 1600's; his speciality was writing gruesome plays foregoing the love and tenderness of Shakespeare and Marlow. Could this be why we see his character feeding the mouse to the cat?