As Temple discusses Princess Ida, he removes all of his makeup with cold cream. At the end of the scene, he removes heavy black eyeliner that wasn't there a moment ago.
Length of Sullivan's cigarette and ash during their lengthy discussion
When Dr. Gilbert is complaining about the telephone, he sits down twice.
This well known quote from the film is a factual mistake: "If you wish to write a Grand Opera about a prostitute, dying of consumption in a garret, I suggest you contact Mr Ibsen in Oslo. I am sure he will be able to furnish you with something suitably dull". The city of Oslo got the name in 1925 - a long time after Ibsen's death in 1906. During Ibsen's lifetime, the capital of Norway was called Kristiania.
The Japanese exhibition that Gilbert and Lucy attend did not open until after Gilbert had started work on "The Mikado". Nor did Gilbert purchase a Japanese sword from said exhibition.
Early in the film, Fanny talks to Sullivan and mentions "the Churchills", and says that "Jennie says that Winston is eleven, covered in freckles and has a total disdain for authority." In January 1884, Winston Churchill was just 9 years old, not 11.
When Gilbert enters the night's take for Princess Ida in his ledger, the date can be seen to be listed as Monday, 10 June, 1884. That date actually occurred on a Tuesday in that year.
Gilbert sarcastically suggests that Sullivan, wanting to write a more serious opera, might try to collaborate with "Mr. Ibsen in Oslo." At the period in which the movie is set, the city was named Christiania.
Fanny Ronalds introduces "The Lost Chord" at her salon as a "new" song in 1884. Actually, Sullivan set an existing poem to his music as his brother was dying in 1877. The song was immediately popular, so much so that Thomas Edison used a recording of it in 1888 to introduce his phonograph machine to London society (and then later recorded Sullivan's response to the recording, which is the only known recording of his voice.)
During the performance, Katisha's kimono is wrapped incorrectly. All Kimono wrap from the right side of the body to the left (i.e. the right side folds over the left), but her kimono wraps from left to right. Every other character has her/his kimono wrapped correctly.