When Clemmie throws the dish of brussel sprouts at Winston the first shot shows the dish up against the wall by the window, in the next shot with Winston the dish is under the drapes.
During the 'Battle of Blenheim' scene, the English soldiers are firing their muskets one at a time. Standard practice of the 1700's was to fire muskets in volleys.
The famous speech Churchill wants to revise (and later delivers in the House of Commons) in the beginning of the film ("To see Mr Gandhi, a seductive Mid-Temple Lawyer ... posing as a half-naked fakir in a manner quite well known in the East, striding up the steps of the Vice-Regal palace to parley on equal terms with the representative of the King Emperor") was actually delivered in 1930, whereas the film starts some years later.
During the 'Battle of Blenheim' scene, the Union Jack is shown as one of the colors of the English army. The Union Jack was only used as a battle-standard after the Act Of Union in 1707, three years after the Battle of Blenheim.