At the end, when Lord Marbury holds up his ambassadorial folder, he is holding it with his right hand gripping the opposite side, in the next frame that shows a full body shot, he is holding it with both hands, one on each side.
When President Bartlet accepts Lord John Marbury as Ambassador he is announced as the Ambassador from Great Britain. The correct title would be Ambassador from the United Kingdom of Great Britain and Northern Ireland.
Several characters in this and other episodes refer to Queen Elizabeth II as "Her Royal Majesty." This is an incorrect form of address. She should be referred to as "Her Majesty Queen Elizabeth," never as "Her Royal Majesty."
When the president is announcing the Swedish ambassador he say "I accept your credence from King Gustaf." His majesty's name is Carl XVI Gustaf, which would makes him King Carl. Or, as the man presenting the ambassador say, Carl Gustaf.
Donna tells Leo that King George III sailed his bride up the river to music that was specially composed. It was King George I who requested a concert on the River Thames, not for his bride but for many nobles who were his companions on the barge. The music was George Frédéric Handel's Water Music.
As Donna and Lord Marbury are discussing Marbury's royal connections, Marbury mentions Edward, Earl of Ulster, who is the son of Richard, Duke of Gloucester. Marbury identifies the Earl of Ulster as being 5 years old. Edward, Earl of Ulster was born in 1974. Thus, at the time the episode aired, the Earl of Ulster was in fact 25 years of age.