Factual error: The American flag displayed when Churchill arrives at the big house to meet Eisenhower has a modern day configuration of 50 stars, not 48 as it was at the time.
Character mistake: King George VI got out of car in admiral's uniform without his cap and saluted another officer. RN officers do not salute without their caps.
Factual error: Throughout the film, Churchill's secretary types his dictation directly on a typewriter incapable of typing at that speed. Even on a computer keyboard, it would necessary to be able to type around 150+ wpm.