Episode #1.2 - S1-E2
Factual error: The settlers prepare to burn Verity at the stake as a witch. Witches were never burned in England or her colonies; they were hanged.
Episode #1.5 - S1-E5
Factual error: The senior police officer's name tag reads "Assistant Commissioner" but he wears the rank insignia of a Deputy Assistant Commissioner.
Factual error: The judge rules in favor of Wendy's father despite not hearing any testimony from his primary witness, who fails to appear. The judge states on the record that he is making this ruling because of the Byrdes' "reputation" rather than any testimony. This is absolutely ludicrous. A judge is not allowed to make a ruling on a child custody case based entirely on his opinion of the litigants, which he doesn't even elaborate upon, rather than any evidence or testimony before him.
Factual error: DI Renton is a Metropolitan Police officer 'parachuted' into Kent to solve a big case. This hasn't happened for many decades. Local police forces investigate their own crimes without help from the Met.