The scene in which The Doctor escapes the executioner's sword, it can be clearly seen that it is not Tom Baker, but a stuntman (Most likely Terry Walsh, who also played the executioner) wearing a wig and similar clothes.
Dialogue between Giuliano and Marco reiterates the myth (popularised by Washington Irving in early 19th-century America) that even the most educated medieval people believed that the Earth was flat. The roundness of the Earth had in fact been demonstrated in Ancient Greece nearly 2000 years earlier.
The doctor wonders how the helix energy got inside the Tardis when it was obviously when he and Sarah were hiding from it and the Tardis door was open.