Factual error: In the scene of King George V's 1934 Christmas Broadcast from Sandringham, there are factual errors. The B.B.C. Engineers are shown operating Outside Broadcast equipment in a room adjacent to the King - but the equipment (BBC Type OBA/8) didn't even come into service until 1938. It should have been type OB/7 in large mahogany cases. Also, the ornate Royal microphone cases were the wrong ones. These were the later (c1937) type first used by King Edward VIII in his Broadcast in 1936.
Continuity mistake: Near the beginning of the film, we see the Duke of York ascending a staircase inside Wembley Stadium prior to doing a speech. Visible out of a window in the stairwell is what appears to be Kingsway (later renamed Olympic Way, commonly referred to as Wembley Way), the road that leads up to Wembley stadium and the Twin towers that were attatched to the building. However, upon entering the stadium, we see the Twin towers over on the opposite side of the stadium and therefore they are on the opposite side of the stadium to Kingsway.
Factual error: Prime Minister Stanley Baldwin is shown resigning due to the failure of the government's appeasement policy towards Adolf Hitler. Baldwin resigned in 1937 as he chose to retire, appeasement continued under his successor, Neville Chamberlain until 1939 when war was finally declared.
Factual error: In the conversation with Bertie after delivering the Christmas proclamation, King George V refers to Joseph Vissarionovich Stalin as "Marshal Stalin". In reality, Stalin was awarded the title of "Marshal of the Soviet Union" in March 1943 after the conclusion of the Battle of Stalingrad and more than 7 years after the death of George V.
Continuity mistake: The balls on top of the red chair change directions throughout the coronation rehearsal scene.