The Masque of Mandragora - S14-E1
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: The nuclear physics in the reactor scenes is laughably incorrect.
The Masque of Mandragora - S14-E1
Factual error: Giuliano makes references to the invention of the telescope. Yet the invention of the telescope was at least a century after the events in the story and Galileo's experiments more than 50 years after that.
The Talons of Weng-Chiang - S14-E6
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.
The Talons of Weng-Chiang - S14-E6
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.
Answer: It was never destroyed on-screen; it was intact at the end of the TV movie, and destroyed by the start of the 2005 series. It was destroyed in the novel "The Ancestor Cell," but in a completely different manner to what happened in the series.
DaveJB