Episode #1.3 - S1-E3
Factual error: Billy is called up into a specific unit of the Royal Artillery. This didn't happen. He would first have been sent to a Royal Artillery training depot and only after training would he have been assigned to a unit.
Episode #1.4 - S1-E4
Factual error: In 1940, all the Americans are leaving London on transatlantic flights. Although the first commercial transatlantic flights began in 1939, they were suspended on the outbreak of war. Real commercial transatlantic service did not begin until after the war.
Episode #1.4 - S1-E4
Factual error: Toby works in the War Office, which is collating all the RAF's losses. The War Office only administered the Army. The RAF was administered by the Air Ministry.