Sherlock Holmes: You have the grand gift of silence, Watson. It makes you quite invaluable as a companion.
Watson points out that one of the vials of liquid in Holmes' possession is "used for eye surgery". In the late 18th century, cocaine was used as a form of medicinal treatment for multiple eye injuries and diseases. In the novels, Holmes is in fact, a cocaine addict. See more...
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Continuity: As Holmes and Watson walk down a street after they've seen Blackwood's grave, we can see a man walking behind them, carrying something over his head. As the shot changes we see him passing them on the left side of Holmes. However when the shot changes again (Holmes says "Inevitably one begins to twist facts.") the man is turning right, behind Watson.
Continuity: In the scene where Watson is moving his things out of the room and Holmes is examining a body, Holmes walks and goes to get a book once he returns, and Watson says "it will probably be a factory by the river" when the camera cuts back to Holmes one side of his shirt collar is down, although both sides were popped just seconds before, and seconds later the collar goes back to being popped.
Continuity: In the scene where Holmes is jumping from the office in the Houses of Parliament, the camera shot from the inside of the office as he jumps out of the window shows that his body is not fully out of the window as he falls down (his legs are still in the room). However, the view outside of Parliament shows Holmes jump clear of the window before he descends to the river.
Factual error: Holmes and Watson's first encounter with the French giant results in a large steel ship, still under construction, being prematurely launched and then sunk. As it sinks, this ship, which is more than 30 meters long, stands on its bow. There is absolutely nowhere in the River Thames near London where the water is that deep.
Character mistake: Near the start, Sherlock reads a newspaper dated Friday November 13th 1890 - that day was actually a Thursday. About an hour later he reads another newspaper dated Friday November 19th 1891. If a week had gone by it should have read the 20th - a year could have gone by, but that date was again a Thursday.
Factual error: In the scene where Holmes is defending himself with some sort of electrical prod, it's clear that the tips of the prod have the same electrical potential (they are connected to the same metal). Subsequently, this device could never be used to shock anyone unless they were standing on a metal plate that was connected to the opposite electrical pole of the prod tips. If it had a Leiden-Jar type power source, it would have been expended after the first jolt.
Continuity: When Irene Adler turns up at Holmes' apartment, Holmes lifts her necklace and we see the Maharaja's diamond hanging off it. When Watson asks Holmes to explain why he jumped through the window after her, when she leaves, we see another shot of her necklace, meant to be the same shot as before. But in the first shot, the diamond is hanging slightly to the left, and in the second, the diamond is perfectly centred.