At the end of the episode, while escaping from Queen Victoria's guards, the Doctor tells Martha that he doesn't know why she's mad at him because he hasn't met her yet. In actuality, her wrath is a result of the Doctor having already met her in season 2 episode 2: Tooth and Claw, in his Christopher Eccleston incarnation.
Because of poor lighting, among other things, in William Shakespeare's day plays were performed during the day. That was why theaters like The Globe had no roofs, so that the sun could light up the stage. It wasn't until much later that performances became a night-time affair.
The architecture of Bedlam is about 100 years out of date.
The Doctor describes the Globe Theater as a "fourteen-sided tetra-decagon." The original theater actually had twenty sides, as well as the modern reconstruction that was used in filming.