Continuity mistake: When the Doctor puts his tie back on after returning from the morning, the collar of his shirt is noticeably askew as a result. Just moments later, when Martha enters the TARDIS for the first time, the collar is neat again, without him having done anything. (00:41:00)
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 the Doctor first enters Shakespeare's room at the inn, the collar of his coat is askew. The scene cuts to Shakespeare, and when it cuts back to the Doctor his collar is now flat, without him having moved his hands from his pockets. (00:09:20)
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)
Revealing mistake: When Lilith bespells Shakespeare to write the end of Love's Labour's Won the way the Carrionites want it, there are several shots where a white fleck of some kind is visible in the lower centre of the screen, stuck to the camera lens. (00:17:10)
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)
Factual error: The establishing shot of Bedlam Hospital shows it with 18th-century neoclassical architecture, in an episode set in 1599, in the Elizabethan era. (00:23:20)
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)
Factual error: The Globe has (and had) 20 sides, not 14.
Character mistake: David Tennant has a strong Scottish accent, and puts on the Doctor's English one. When David and Freema Agyeman are lying on the bed in the hotel, David forgets his English accent when he says, "There's something I'm missing, Martha."
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.
Continuity mistake: In the episode "New Earth", the Doctor said that the titular planet is in the galaxy M87. Upon returning to New Earth in this episode, he says that the planet is 50,000 light-years from where the original Earth used to be. That's a difference of over 50 million light-years, since M87 is a very real galaxy in the centre of the Virgo Cluster, that far away from the Milky Way. (00:02:55)
Revealing mistake: After arriving in New New York's undercity, the Doctor and Martha find a screen playing the news. The Doctor tinkers with it and gets a video of flying cars passing a picturesque view of the city. This is a clip from the last episode set on this planet, "New Earth" - the fact that in a close-up of the screen, the TARDIS can be seen parked on the cliffs as it was in that episode clinches it. (00:03:55)
Continuity mistake: After Milo and Cheen abduct Martha, they put a sleep patch on her before entering their car. In the close-up where Cheen applies the patch, it's stuck on securely and neatly, with the top and bottom of the square pointing directly at Martha's head and chest respectively. In a wide shot immediately afterwards, the patch is stuck on quite loosely and has gone askew. (00:06:35)
Continuity mistake: After the Doctor gets directions to the motorway, when the red-haired female pharmacist leans over her counter to try and persuade him to buy some Happy, her hands change position between shots. (00:08:00)
Continuity mistake: The registration of Milo and Cheen's car is shown on the computer screen and stated aloud as "4-6-5-◊-6." However, there is a shot of Martha and Cheen looking out the window where the car's registration sticker is visible, showing a different registration: "9-9-6-γ-1." (00:13:15)
Continuity mistake: When the Doctor, after being placed on hold while attempting to call the police, talks to Brannigan and Valerie about other people he could contact, in close-ups, Valerie has her right hand resting on the top of her seat. In a wide shot, she lowers her hand, but in the next close-up of her, it's jumped to its previous position. (00:14:20)
Plot hole: Martha tells the kidnapping couple to switch off all their engines so the Macra don't notice them. Yet during this scene, the car remains hovering above ground, meaning the engines must be engaged in some way, and the Macra should still hear them. And these things don't hover when deactivated - the car was shown to be parked on the ground at the start of the episode.
Chosen answer: No, no information is avalible for the identity of the entity.
Repo_Man