At the ball, Franz Joe see was introduced as "His Majesty" but as Emperor of Austria and King of Hungary he was also referred to as "His Imperial and Royal Majesty"
The tune still used as Germany's national national anthem was originally used by Austria-Hungary, so it's use to introduce the Emperor at the ball is not an error.
At one point in the story, Sherlock Holmes encounters an American lawman named Eliot Ness (who in reality was to win fame in the 1920s for his efforts to enforce the Prohibition laws). Ness does tell Holmes that this is his "first case" in which case he must have been very precocious, the story is set in 1910, while Ness was born in 1903, which would have made him seven years old at that time.
In Part 2 of the DVD release, at approximately 44:20, when Dr. Sigmund Freud is talking with Irene Adler about her dream and it's meaning, the reflection of a boom operator can be seen several times in the glass of the cabinet in the back right hand corner of the scene.
In an early scene, a reflection of the mic can be scene in a cabinet with glass doors. It is slowly withdrawn from sight before the scene is over.