Continuity mistake: In the scene where Watson and Adler are laying out the map, they place two objects on the map to hold it down. In the very next clip where it shows Holmes talking, you see Watson and Adler placing those same objects on the map.
Continuity mistake: At the graveyard scene, when Holmes borrows Lestrade's pen you can see that he has unbuttoned cuffs, and a pair of cuffs underneath. When he takes off his hat and scratches his head in the very next frame, he has just bare skin under his unbuttoned cuffs.
Factual error: In the scene depicting life on Baker Street (after the "Sherlock Holmes" title), a horse-drawn carriage races through the streets of London. The only problem is, the carriage is driving on the right side of the road with others passing on the left. In England, carriages would be driving on the left. (00:07:05)
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.
Factual error: When Holmes and Watson arrive in Nine Elms you can see Tower Bridge in the background. This wouldn't be possible due to how the river Thames bends, and to the fact that Tower Bridge is several kilometers away from Nine Elms.
Plot hole: After the scene at the Houses of Parliament where Irene Adler escapes through the sewer from the clutches of Lord Blackwood, she suddenly appears at Tower Bridge, about 3 miles away. Even assuming she ran there and the journey was skipped, going there makes zero sense. It slows her down, leaves her exposed and limits her exit points - she's got all of London to escape into! (01:48:00)
Continuity mistake: When Holmes and Watson get off the boat onto land, they wade through water for a short distance. But in the next shot when they're inside, neither of them have wet clothes.
Character mistake: In the scene showing the outside of the hotel the British flag is flying upside down. The wider white band on the white X has to be top left next to the top of the flag pole. It is at the bottom, which is a universal distress sign.
Continuity mistake: 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. (01:16:45)
Character mistake: When Holmes is being chased through the boatyard by the giant, he trips over the ship's mooring chain. The links are over a foot long, and should weigh 100 pounds each, yet the whole chain jiggles like it's made of Styrofoam.
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.
Revealing mistake: When Holmes is looking at the white mark on Watson's fiance's ring finger in the restaurant, shortly afterwards a blue flashing light goes past the window.
Continuity mistake: 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. (01:38:45)