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.
Last of the Time Lords (3) - S3-E13
Deliberate mistake: The Master uses his laser screwdriver to suspend the Doctor's ability to regenerate. While he is in fast motion, in a close-up you can briefly see Lucy's arms in fast motion as well. (00:12:20)
Chosen answer: No, no information is avalible for the identity of the entity.
Repo_Man