When King George VI says, "I'll get her [Princess Elizabeth] to marry a Greek or someone," this is a reference to Elizabeth II's real-life marriage to Prince Philip, Duke of Edinburgh, who was born in Greece as the son of Prince Andrew of Greece and Denmark.
The real life Winston Churchill was actually half-American. His mother Jennie Jerome (Lady Randolph Churchill) was born in Brooklyn in 1854. His grandfather, Leonard Jerome was a New York State Assemblyman.
This comedy uses as a running joke the Hitler one testicle gag from a version of "Hitler Has Only Got One Ball" lyrics sung to the Colonel Bogey March. It's even seen performed at a London concert much to Hitler's chagrin. The lyrics for the version performed here are:
"Hitler has only got one ball,
Göring has two but very small,
Himmler is somewhat sim'lar,
But poor old Goebbel's got no balls at all." Hitler's high-ranking off-siders Goebbels and Göring appear in the film.
The Adolf Hitler character is mistaken for Charles Chaplin on more than one occasion in this movie. Once by a cab driver and once by the King, Hitler is the subject of mistaken identity joke for Chaplin's the Tramp character from the classic silent comedy The Gold Rush (1925) where he is remembered for eating his shoe. Interestingly, it is of note that Chaplin spoofed and parodied Adolf Hitler in his later movie, The Great Dictator (1940),
On the DVD commentary during the scene where US Churchill and Denzil Eisenhower exit the British War Office: director, Peter Richardson, dubs, "This is very r... relevant to the Iraq War".