Character mistake: In the opening scene, Sherlock makes a point to correct Barry's poor grammar. But later, when talking to Watson, Sherlock uses poor grammar by saying "who's sleeping with who." It should be "who's sleeping with whom." Not a mistake Sherlock would make.
A Scandal in Belgravia - S2-E1
Continuity mistake: We see John come into the room and stand next to Mrs. Hudson and put on his coat. After a few shots Mrs. Hudson walks away with the plates and says, "Lovely tune, Sherlock..." As she's walking away we see John isn't wearing his coat, and he puts it on again. (00:50:00)
Continuity mistake: As Sherlock and John approach the missing subway car, and especially as they bend to peer beneath it, the interior of the car to a distance of several feet is plainly visible through the window of the door (you can see the curved ceiling inside and some unlit fluorescent light bars). However, an interior shot then shows that there is a closed door inside the car, a foot or so inside the exterior door, that Sherlock has to push open to enter the car proper. This door should have blocked their view of the inside of the car before they entered. It didn't, so it has gone from open to closed between shots without anyone touching it. (01:05:35)
The Hounds of Baskerville - S2-E2
Deliberate mistake: The army major wears a full beard. British Army personnel may not wear beards. (The beard is a nod to the original canon character on which he's based, John Barrymore, who is described in the book multiple times as being a "black-bearded man").
Factual error: A jury in Hamburg is asked if Mr Troppoff is guilty. There are no juries at all in the German court system.
Factual error: In "The Bloody Guardsman" case, Bainbridge, who is in the Welsh Guards, is referred to by everyone, including himself, as "Private Bainbridge." The Foot Guards use the rank of Guardsman instead of Private.
His Last Vow - S3-E4
Continuity mistake: When Sherlock is being rushed to the hospital, when the paramedic rips open his shirt the body has body hair, but all the topless scenes following show that Cumberbatch has a hairless chest.
Factual error: In a couple of scenes with the mobile phone when Sherlock is talking to the girl and she hangs up, the soundtrack has a audible "dial tone" inserted. Mobile phones don't have dial tones.
Plot hole: For the supposed code that hacks into UK system, Sherlock deduces that the finger taps are counted as 1s in the binary code and the rest (while Moriarty's fingers are in the air) are taken as 0s. Sherlock can't know the rate at which the rests are counted in the binary code that he thinks Moriarty tapped out. So even if the key code was real, he wouldn't have known what it was.
Character mistake: While the original Sherlock Holmes is famous for making water-tight deductions, the one in this episode does not quite live up to that standard. He declares someone a "compulsive cheat," because: "Waterproof cover on his smartphone. Yet his complexion doesn't indicate outdoor work. It suggests he's in the habit of taking his phone into the shower with him, which means he often receives texts and emails he'd rather went unseen." There are far too many problems here. (1) The only type of complexion that indicates outdoor work is sunburned. We don't have water-soaked or snow-frozen complexions. So, yes, he might work outdoors. (2) Indoor work may also deal with water, e.g. plumbing, dish washing (note what the accused man is doing!), water purification, lab work, etc. (3) Some people might just purchase a waterproof cover as a precaution. Some might receive it as a gift. Some may receive it free during a bulk purchase. (4) Not everyone who takes his or her phone into the shower has fidelity problems. They might want to listen to music, be up-to-date with the stock market, or, if I may use a euphemism, might want to have some quality alone time. (00:12:35)
Character mistake: Lestrade mentions that there could be some "poor sod covered with semtex on the streets somewhere" when talking about Moriarty's victims, but semtex does not go off via gunshot, much like C4. But that is what happens when one of the victims dies however, so the explosives are not semtex.
Suggested correction: The term "Semtex" is often used to refer to any plastic explosives, much like the term "Hoover" for a vacuum cleaner or "Kleenex" for a tissue.
But that doesn't negate the mistake.
Other mistake: Watson never orders, but somehow while in Angelo's, he has a full plate of pasta.
Factual error: In "The Bloody Guardsman" case, the guardsmen are on sentry duty unarmed. Sentries always carry rifles.
A Scandal in Belgravia - S2-E1
Other mistake: While Sherlock sits reading the paper he gets a text alert from (we assume) Irene Adler, and John notes that he had heard this alert fifty seven times. At the end of the episode, when Sherlock is looking through the texts that she sent to him, there are not that many texts from Miss Adler.
Continuity mistake: When Sherlock pulls the gun on Moriarty in the pool scene, he is holding it with two hands but then puts one hand down. In the next shot, he has two hands on the gun again. Then again in the next shot he only has one hand on the gun.
Factual error: The entire reason Sherlock takes up the case is because he is intrigued how a man managed to disappear from a tube carriage in between stations - it appears to be impossible to do. However, any Londoner will tell you that it is perfectly simple to do: all tube carriages have doors between them linking them. So if the man wanted to leave the carriage between stations, he'd just use the door at the end of the carriage. The train employee would not be puzzled by this, nor would Sherlock consider the case worthy of his time.
Character mistake: When Sherlock receives the phone, it is in a hand-made paper envelope. He says "Nice stationery. Bohemian" and specifies "From the Czech Republic." The paper is Losin, which is produced in Velke Losiny paper mill, the oldest in Europe and the only Czech one. However, it is not located in Bohemia, but in Moravia, which is a different region. It is an equivalent of calling Glenfiddich "English whisky from Britain." An error Sherlock would not make. (00:11:45)
Continuity mistake: Sherlock turns over the note on the body to read it, then puts it back down face up. When Watson goes to look at it, it is face down again. (00:50:10 - 00:50:35)
Continuity mistake: At the end of the episode when Sherlock takes the explosive jacket off John, he throws it away from them both. You can see the jacket change places during each camera shot. (01:27:10 - 01:28:02)
Revealing mistake: Early on in a close up of John Watson, you can clearly see the mesh of the fake moustache.
