Factual error: The first Kinetoscope (arcade of 'personal movie viewers') was opened in 1894 and the first motion picture studio was located in New Jersey. There is no way that they would have known enough about motion pictures in 1887 to go into them, let alone go to Hollywood to do so. And the use of the word 'movie' is at least twenty years too early.
Factual error: Several real-life events are off in the movie's timeline. The movie itself is set in 1887, yet it includes Arthur Conan Doyle beginning writing Sherlock Holmes, although he did so before 1887; a mention of the Savoy Hotel, which was not built until 1889; and many references to and an appearance from Jack the Ripper, who was not active until 1888.
Continuity mistake: During the fight with the street gang, Jackie Chan is about to jump onto the cloth roof to send a gang member flying away. Watch the first half of the shot (from behind Chan) and the cloth in the section Chan is about to jump into is hanging down in the space between the joists and is very slack. When the shot changes from the front to show Chan jumping and landing into the cloth, the cloth is now stretched tight for his landing.
Continuity mistake: When Chon Wang is spinning the wheel back and forth causing Roy to be dunked into the water again and again, in one shot, the timing of Wang turning the wheel doesn't match up with Roy actually dunking into the water. It is the shot where it happens several times, timed to match the music in the background.