Corrected entry: During the final parts of the movie, while the King is addressing all of the nations, the movie shows different families' reaction to the speech. The error comes when they show Lionel Logue's family. By this point in the movie, Logue's children are teens/young adults (proven by scene showing Logue's son,grown now, driving Logue to the palace to help King George deliver the final speech). However, the family is shown with Logue's children being alot younger.
Corrected entry: The correct name of the second child of the Duke and Duchess of York (younger sister to (now) Queen Elizabeth) was "Princess Margaret Rose". She is incorrectly mentioned in the film as simply "Princess Margaret" a name by which she did not come to be known until she became an adult.