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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Continuity mistake: At the end of the film, in the bridge confrontation between Holmes, Blackwood and Irene Adler, Lord Blackwood forces Adler to the edge of a precipitous (and deadly) fall into the Thames. There is even a perspective shot, looking straight down, of her heels teetering on the edge and nothing between her and the river except two sailboats far below. There are obviously no scaffolds or other means of obstructing her fall in this shot. It's a dead drop. Then Blackwood shoves her straight backwards over the edge. But, when Holmes looks over moments later, Irene Adler is safe and sound on a convenient bit of scaffolding that magically appeared just a few feet below.
Continuity mistake: When the big guy runs up to slipway 5 he passes a group of men and a horse in front of the door. When he opens it the camera is in front of him and behind him is a group of men and a horse and a wall and piles of crates that are nearly touching the horse - these have appeared from nowhere.