Factual error: ACC Pat Gallan wears the ribbon of the Queen Elizabeth II Diamond Jubilee Medal. The medal was issued in 2012. Her medals would be correct for 2017 when the series was made, but not 2007 when it is set.
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.