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)
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.
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.