When Kane tells correspondent Cole it was cold at basic training, his arms are up and then the next shot they are down.
Almost halfway through the show, a German [actually US M3] half-track stops next to a road sign that shows "St Lo 50 KM Caen 20 KM" This would put them around Thury-Harcort, which was liberated by the British 59th Division in August 44.
When Hanley lights a cigarette at 10:17, it's a modern-day filter cigarette with gold band, not the usually-shown non-filtered ones that were the only kind available in those days.
When Saunders is wounded in his arm, the bandage is wrapped around the outside of his jacket sleeve.
When the half track pulls up you can see the mic in the upper left corner.