Factual error: In the fight scene where Jackie Chan and Donnie Yen fight on the boat right after Yen starts firing the gatling gun, Chan kicks him away from the gun and the gun keeps going. A gatling gun stops firing when the trigger is released, and a new gun such as that one isn't going to have problems with it "sticking" down.
Factual error: Before he became the famous writer, Arthur Conan Doyle was an ophthalmologist, not a detective.
Deliberate mistake: When Chon throws Roy's "plan" into the fire, you can see the drawing and plans have mysteriously vanished from the parchment.
Factual error: In one of the first shots of London, there is an aerial view of the River Thames that shows the bridge leading to Big Ben and father upstream Tower Bridge. 2 problems: the movie is set in 1887 and Tower Bridge was not finished until the year 1894, and secondly, from that shot, Tower Bridge would be below Big Ben, off screen, not above it.
Factual error: It is British law that a non-British (or Commonwealth nowadays) citizen does not receive the title of "sir" as part of their knighthood. Therefore, Chon and Roy would not be referred to in this manner during the knighthood ceremony.
Revealing mistake: During the final sword-fight, in at least two shots, when the camera is facing Chon Wang and Rathbone's back is towards camera, you can tell that Rathbone is being played by an Asian stunt-person for certain moments. His hair doesn't match perfectly, his body type is SLIGHTLY different and you can even occasionally catch very brief glimpses of the stuntman's face in shots where he twirls around. (Most noticeable early on in the fight during the stunt where Chon jumps up onto the railings after blocking and dodging several swipes from Rathbone).
Revealing mistake: During the "Singing in the Rain" segment of the big fight after Chon and Roy arrive in London, watch carefully when Chon "lifts" himself with one arm, raising his legs to the side to dodge a strike. It's clear that wires were used, as his body somewhat unnaturally lifts up. (00:31:15)
Factual error: All the cars used in the film have pneumatic tyres. The film is set in 1887 and pneumatic tyres were not successfully used on cars until 1895.
Factual error: Early, rotating-barrel machine guns were all activated by cranks, not buttons or triggers as shown in the film. While there were prototypes of trigger-type machine guns such as the Maxim, under development at the time, they were very different in operation than the Gatling-type gun used in this movie.
Continuity mistake: When Jackie's sword gets thrown into the gears of Big-Ben, the way it lands doesn't match the way it falls.