Though very photogenic, the C96, or "Broom handle," Mauser pistol, used extensively in this film, was first produced in 1896, thus would not have been available in 1891. Also, most models of C96s had a non-removable internal magazine, which would have been loaded from above with a stripper clip. It wasn't until the early 1930s that the C96 design would be modified to accept a removable magazine (conveniently loaded from the bottom, as pointed out in the film).
Holmes follows Moriarty's lecturing tour across Europe and mentions Oslo, Norway. However, as of 1891, Oslo had been called Christiania since the mid-1600s. It was not called Oslo again until the 1920s.
Watson relates the story by typing on a typewriter, which is shown at the beginning and end of the movie. He is clearly using an Underwood No. 5, a classic typewriter. However, this typewriter did not exist in 1891, and even the Underwood model No. 1 had not yet come out.
The German flag shown on the boxes is the current German flag and probably used for the benefit of the audience. It was first used 1848-1866 in the Deutscher Bund, but by 1891 a different flag was in use, with black at the top, white in the middle and red at the bottom. It was the flag of the North German Confederation (Norddeutscher Bund) 1867-1871 and the German Empire (1871-1918). After that, in the Weimarer Republic (1919-1933), black-red-gold was the official flag again.
When Holmes and Moriarty are playing chess, Moriarty says "Your clock is ticking, may I remind you this is blitz chess." The earliest known usage of the term 'blitz chess' according to the OED is in 1942, 51 years after the film is said to be set.
Upon arriving for Watson's stag party, the band is entertaining the party-goers with "The Band Played On", which was written in 1895 by Charles B. Ward, lyrics by John F. Palmer and, therefore, could not have been heard in 1891.
At the telegraph office, the word "Telegraphen" is spelled with "ph" on the wall in the background, but with an "f" ("Telegrafenamt") on the door itself. Although both spellings are correct in modern German, the "f" variant was not used in the 19th century but came up much later.
In the Arms Factory Scene, Col. Moran introduced the c96 Mauser pistol as a 'machine pistol, self-repeating'. Machine pistols are automatic firearms which fires burst of bullets when the trigger is held. Even if the c96 was available (which actually wasn't until 1896), it was a semi-automatic pistol at that time, firing one round when triggered. The c96 was first converted into a automatic variant in 1932, designated M712 Schnellfeuer.
During the final dance scene, Dmitri Shostakovich's "Suite for Jazz Orchestra No. 2" plays. Shostakovich did not write the piece until 1938, when it was written for the State Jazz Orchestra, in Moscow.
During the establishing scene of Baker Street near the start of the film construction workers are seen in the street. A sign says, "'UNDERGROUND' Railway Construction Keep Out". In 1891 the railways being constructed under London were yet to be collectively called 'UNDERGROUND' and the logotype used on the sign, with the larger initial U and final D, was not seen until 1908.
When Watson first goes to Holmes' flat, Mrs Hudson hints that she is concerned at Holmes' mental state but suggests a stay in a "sanatorium". This would instead imply he needed rest and treatment for tuberculosis, which is what was provided at a sanatorium. The word was only later, and especially in the USA rather than England, also used to describe a hospital for those with a mental illness.
Although the English flag does feature St. Goeorge's Cross, in 1891 there was no particular connection with England. At that time, the Union Jack would have been used to identify the United Kingdom. Moreover, the term used would have been 'Großbritannien' (in reference to the United Kingdom of Great Britain and Ireland) instead of 'England'.
The pistol that Claude Ravache (Thierry Neuvic) shoots himself with in 1891 is a French Mle 1892 Revolver that was in service from 1892 and 1924 and was issued to officers in the French Army, Navy, and National Gendarmerie, amongst others.
When the gang is running from the Germans through the forest, one of Moriarity's German lackeys yells that it is time to introduce them to "Little Hansel" (in subtitles). Strangely, what he really yelled was, "zu viele Füchse für die kleinen Hühner," or "too many foxes for the little chickens".
Professor Moriarty is described at one point as "a Professor at Oxford University." But when Holmes accepts an invitation to visit Moriarty following Dr. Watson's wedding, the lead in shot shows King's College at Cambridge University.
When Watson first enters the house to visit Sherlock, he is clean shaven (other than the mustache) and has a clean haircut. When he is in his old office viewing the diorama, he has five o-clock shadow and his hair his longer and messy. After viewing the diorama, when Watson is shown to attend to Gladstone, he is again shown with the cleaner hairstyle and freshly shaven appearance.
When Holmes entered Mr. Moriarty's office to get an inscription, there is a chessboard on the desk, with all pieces at their starting squares. White's King and Queen starting position is wrong. White Queen should be on white square, opposing the black Queen on the other rank.
When "Little Hansel" is fired, the slow-motion shows boiling red flames and black smoke emanating from its muzzle, which are obviously gasoline-fueled. The only artillery shell propellant in use at the time would have been gunpowder, which produces a brief flash with cinders and white smoke, but no flames.
Although displayed correctly, the flag of Prussia seems out of place since in 1891 the Kingdom of Prussia was part of the German Empire, represented through the (incorrect) German flag in the same room.
When Dr. Watson first visits Holmes at his home, he is struck by a dart in the back. Later, a rectangular pad can be seen protruding from underneath Watson's jacket where the dart is stuck, before Holmes pulls it out.
A German sign on the door of a chemical lab in Heilbronn warns of "Lebensgefahr" (mortal danger), but then has the English word POISON in large red letters in the middle. It makes no sense for the most important word in a sign to be in a foreign language, and is clearly for the benefit of the audience. (The skull & crossbones symbol might have been used, as it was internationally recognized by the 1880s.)
The goof items below may give away important plot points.
At the end of the movie, Moran shoots a dart from his cane to kill Rene'. He preloaded the dart into a modified rifle cartridge which has a headstamp marked 223 REM. The .223 Remington cartridge is the civilian version of the 5.56 cartridge used for the M-16 who's earliest date is from the 1960's. Although the loading process seems complex for a simple dart, there's no evidence of a primer or powder that would have fired the dart.
Before crossing borders from France into Germany, Mary's scarf is given away. At the end of the movie, Watson is wearing it again. The scarf had been given to one of the gypsies who accompanied them on horseback; this gypsy is the only one who survives the escape and makes it to the train with them. The scarf is then used as a bandage on Holmes' arm in the train. We can safely assume it was then given back to Watson by Holmes.