Factual error: Giuliano explains to Sarah that he thinks the world is round as though this were radical. But this was the common belief throughout the late Middle Ages. The argument was about how big the Earth was and the ignorance about the existence of a continent between Europe and Asia.
Factual error: When The Doctor questions the arrested Chinaman in the Police Station (in episode one), the Doctor claims to be able to speak several Chinese dialects. What the Doctor actually says to the Chinaman is "How Are You?" in Cantonese, but the rest of what the Doctor says is completely improvised gibberish that SOUNDS Chinese, but is, in fact, complete nonsense.
Factual error: The Doctor mentions at one point in the story that he had once been fishing in the River Fleet with the Venerable Bede. The Venerable Bede was a distinguished 7th century scholar, who lived his entire life at Jarrow, on Tyneside, and never at any time came to London.