When The Queen receives the news of the Death of Sir Winston Churchill, she is at a small family gathering celebrating the birthday of her uncle HRH Henry Duke of Gloucester. Churchill died in January 1965, The Duke of Gloucester was born in March, so unless it took a full two months to be told, then this is clearly a factual inaccuracy.
It's 1964 when Blunt is arrested and two Rover 3.5 cars turn up , but one of them has the UK 'C' suffix on the number plate which is actually for 1965.
During the dinner and birthday party scenes, the closed captioning refers to his character as the Duke of Kent. However, Prince Henry was the Duke of Gloucester, not Kent.
Princess Margaret had blue eyes and was correctly portrayed in the first two seasons. Helena Bonham Carter has brown eyes.