Audio problem: When the Doctor and Martha are watching Shakespeare in the Globe, Martha says "He's a bit different to his portraits". After she says this on the left of the screen the Doctor's head comes into shot and you can clearly see by his facial expressions he is saying something to Martha, yet no sound is heard. (00:06:10)
Continuity mistake: When Lilith runs her hand along the side of the Doctor's head to distract him so she can get some of his hair, in the wide shots her fingers are extended past his ear. In a shot facing him, however, her fingers are curled and in front of his ear. (00:34:40)
Continuity mistake: When the Doctor is persuading Shakespeare to come up with some words to stop the Carrionites with, in wide shots he has his right arm around Shakespeare's shoulder and is holding his left arm. In close-ups, they are not in physical contact. (00:38:35)
Continuity mistake: When Lilith has Shakespeare under her spell and is having him write an alternate ending to his play, there is one shot of his face where his quill can be seen in the corner, perfectly still, even though the next shot shows that he's writing. (00:18:25)
Continuity mistake: When the Doctor, Martha and Shakespeare are in the Globe and they talk about the theatre's architecture, there is a wooden staircase in front of the stage, which Martha and Shakespeare use to descend from the stage when the three leave. Shortly after, at the beginning of the scene where the two actors from Shakespeare's company accidentally summon a Carrionite while practicing their lines, the staircase is gone. (00:22:10)
Deliberate mistake: The Globe Theatre is shown staging performances at night. In actuality, they performed during the day, when there was enough light, since this was pre-electricity. This was done both to make the climax of the episode scarier and because they shot on location in the real Globe, which still shows its plays during the day, and thus they didn't have a lot of time to shoot during the day there.
Character mistake: After the Carrionites kill Lynley, the Master of the Revels, by using the doll to make him drown on dry land, the Doctor says, while examining the body, that he's never seen a death like it. In the Third Doctor serial "The Mind of Evil", involving a monster that could make people relive their worst fears, a character died in exactly that fashion. (00:13:10)