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. (00:27:20)
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: When Will shouts "Follow that boat!" a motorboat speeding by is visible in the lake.
Factual error: Throughout the story, the threat is that Viola is going to be shipped off to Virginia with Lord Wessex. Virginia did not exist until 1607, a good 20 years after this story was set.
Continuity mistake: In the tavern scene, when Shakespeare and Marlowe are speaking, there is a bartender. In the shot in which Marlowe says, "His best friend is killed in a duel by Ethel's brother or something. His name is Mercutio", the bartender starts looking at Marlowe, and by the end, he turns his eyes towards Shakespeare. In the next shot, when Shakespeare says, "Mercutio... good name", the bartender's face has immediately turned toward Marlowe, without any time to do so.
Factual error: Two scenes show aerial views of the cast in a church: this is in fact St Bartholemew The Great in the Smithfield area of London. These show everybody walking on the floor of the church, which is made of Victorian tiles, laid down in the nineteenth century, about 300 years after the age of Queen Elizabeth I (played by Judi Dench) and William Shakespeare.