Several times during the film, Churchill's car alternates from having blackout headlights to having normal unshielded headlights.
In the breakfast scene where Churchill "clears the table" he stands to refill his glass from a bottle. First he picks up the bottle in right hand and holds glass in left. Next shot he is holding glass in right hand before resuming scene with bottle in right hand and glass back in left.
Prime Minister Winston Churchill announced that he would go to sea with the fleet and watch the D-day landings from HMS Belfast. This idea was opposed by many and it took King George VI to stop him, by insisting that if Churchill went he would also go. Eventually that made Churchill back down.
Montgomery is wearing a field-marshal's uniform when he was at the time a general. He was promoted to the rank of field marshal on 1st September 1944.
When King George VI salutes Eisenhower in Naval uniform, he actually does an Army salute. Also the King is not wearing his cap when exiting the car on arrival and therefore would not have returned the soldiers salute.
General Ismay was Churchill's primary military advisor during the whole of WW2, General Smuts was a member of the War Cabinet and may have advised Churchill closely, but he had other responsibilities and it was Ismay's job to persuade Churchill on matters of military advice, which he had to do frequently.
Churchill was not present when Eisenhower was deciding on whether or not to go ahead with D-Day.
During the first meeting with Eisenhower, the US flag flying over the grounds has the current 50-star pattern. In 1944, Alaska and Hawai'i were not yet states and the US flag had 48 stars.
The song Happy Days Are Here Again came out in 1929. It is unlikely that the two daughters of Churchill who were in their teens at the time would have been bouncing along to a song that was ten years out of date. By then, American swing was the most popular among the youth.
Churchill speaks of distracting the Germans or spreading their forces thin by invading elsewhere in Europe, apparently ignorant of Operation Fortitude, which involved a counterfeit army that appeared to German reconnaissance to be aimed at Calais rather than Normandy.
Bernard Montgomery was notably short at 5 feet 6 inches, shorter than Dwight Eisehower (5'10"). Julian Wadham (5'11") playing Montgomery is taller than John Slattery (5'10") playing Eisenhower.