1998 was the only year that two performers were nominated for Academy Awards for playing the same character in two different films: Judi Dench was nominated (and won) for Best Actress in a Supporting Role for playing Queen Elizabeth I in Shakespeare in Love (1998), and Cate Blanchett was nominated for Best Actress for portraying Elizabeth I in this film. Joseph Fiennes and Geoffrey Rush appeared in both films as well.
Sir William Cecil, Lord Burghley, served Elizabeth for most of her reign as Secretary of State and Lord Treasurer. He continued to advise her up until his death in 1598. He was only 38 years old when Elizabeth I was crowned, not the old man depicted in the movie.
The costuming and shot composition of the coronation is based on Elizabeth's coronation portrait. For example, Elizabeth is shown wearing her hair long. This is historically accurate, as the real Elizabeth was giving the public a sign of her virginity.
Though depicted as an elderly married man here, The Earl of Arundel was in his late forties and unmarried when Elizabeth ascended to the throne. He was also one of her suitors, making himself look ridiculous in his expenditures on clothes and bribes for Elizabeth's ladies. However, he never stood a chance, as Elizabeth thought him ugly and buffoonish.
The Duke of Norfolk (Christopher Eccleston) doesn't actually do much, despite being the principal villain. So, in order to create a sense of action for him, director Shekhar Kapur chose to show him in motion as much as possible.