Episode #1.1 - S1-E1
Factual error: The American flag shown waving outside the White House is the current present-day flag with 50 stars. From 1896 to 1908, (the time period that this show is set in) the US flag only had 45 stars as Oklahoma, New Mexico, Nebraska, Alaska and Hawaii were not recognised as states in that time period. The flag did not have 50 stars until 1960. (00:04:30)
Factual error: Sir John Franklin's wife is consistently addressed and referred to as Lady Jane. Since she only held a title due to her husband's knighthood and not in her own right, she was actually Lady Franklin. Nobody in the circles in which she moved would have addressed or referred to her as Lady Jane.