The cigarette that Richard smokes is an Abdulla - a non-nicotine herbal cigarette. The props department managed to find six remaining packs in London and bought one packet intact (of 30 sticks).
Since the film is set in the alternate 20th-century, Ian McKellen had some trouble of setting the location for Act 3 Scene 1, where the Prince of Wales meets Richard before being sent to the Tower. Someone suggested that the royals usually arrive in London by rail. The scene was eventually known to everyone in the film as the 'Victoria Station' scene.
Ian McKellen made Queen Elizabeth an American because this way, her family and herself could be seen as social-climbers, from commoners to royalties. It also suggests an alternate history where Edward VIII (a British King who reportedly admired the Nazis) was able to keep his throne while marrying the scandalous American social climber Wallis Warfield Simpson. In real life that didn't work, and those two became known as Duke of Windsor and Duchess of Windsor.
Duchess of York: [to Richard III]
To war take with you my most gravest curse! My prayers shall on Richard's party fight. Bloody you are! Bloody will be your end! Shame serves your life and will your death attend.