Factual error: Percy Bysshe Shelley's father was a baronet, not a peer. He was Sir Timothy Shelley, not Lord Shelley as he is referred to here.
Factual error: Many elements of Marlott's trial and execution are incorrect. The judge sits with two assessors (a European practice, not a British one). He is addressed as 'Your Honour' instead of the correct 'My Lord'. He instructs the jury to find Marlott guilty and then goes straight to sentencing, which would never happen; a judge can instruct a jury to acquit, but not convict. He puts the black cap on himself, instead of an attendant doing it. The form of words for the death sentence is incorrect. The chaplain (who appears to be Catholic, not Anglican) gives a speech at the scaffold.
The Frankenstein Murders - S1-E5
Factual error: When Mary looks at the newspaper, it says "Tuesday, March 31, 1827." But that was a Saturday.
Prodigal Son - S2-E1
Factual error: Dipple refers to a statue and guesses it to be of Vishu from West Bengal. Truly that art form is still found in present day Bihar, West Bengal, Orissa but it is also found in Southern India. However, the guess is wrong on two accounts, first, Vishnu is a male deity but the statue was that of a female deity. Second, West Bengal came into existence after 1947 (or at least 1902) so there cannot be any concept of West Bengal back in 1820-30. At that point there was only Bengal. (00:25:45)