Continuity mistake: When Sherlock is backstage at the circus and finds the yellow spray paint, he draws a line on the mirror. In the next shot, the line he drew is completely different (and in fact is more of a squiggle). (01:07:40)
Revealing mistake: When they are watching for vases, the auction website has no proper domain. It is loaded locally from the C:\ drive. (00:55:00)
Continuity mistake: After receiving the third pip. Dr. Watson turns on the television to the news. During the news segment, it states the age of Connie Price as 48. Then in the scene immediately following, DI Lestrade says she was 54.
Visible crew/equipment: When Sherlock and John get into the taxi in Baker Street (leaving to go to the scene of their first case) you can see a filming crane reflected in the back of the taxi.
Revealing mistake: While Watson and Sherlock talk about the deceased banker and the crime scene photographer takes pictures of the dead body you can see the "corpse" breathing, as the buttons on his waistcoat are moving. (00:14:50)
Other mistake: At the end of the episode, the evil Shan is texting with (most likely) Moriarity. She is sitting at a desk facing a wall and yet the laser targeting ray appears directly on her forehead, which could only come through a window directly opposite her.
Continuity mistake: When Sherlock and Watson first get to the bank, the time for New York is 7:45, then when Sherlock is trying to find out who the message is for, the time for New York is 7:20.
Revealing mistake: Before John Watson closes the laptop, the screen displays a phone tracking website in the Chrome web browser, supposedly at Mephone.org.uk. In the URL address bar, however, "file:///C/http/mephone.org/mephone.html" is visible which is a standalone HTML file on the computer's hard drive. (01:08:35)
Revealing mistake: The banker shoots himself with a Sig 226R. When you see it lying on the bed it has a screw missing from the grip. In the first episode, Watson has a gun in his desk drawer. It is a Sig 226R also with a screw missing from the grip. Obviously they only have one prop gun.
Revealing mistake: In the bank where Sherlock is trying to get a view of the painting with the Chinese numbers, he backs into a pillar, which wobbles. (00:11:25)
Continuity mistake: In the opening scene when John is going to the refrigerator, a white skull can be seen on the left side of the kitchen table amongst all Sherlock's science equipment. When he closes the refrigerator door again after discovering the severed head, the skull has disappeared. As he's leaving the kitchen, the skull reappears. (00:03:25)
Continuity mistake: When Sherlock steps out of the taxi on Baker Street three extras walk by. First, it's a lady with her back to the camera, wearing a dark jacket, purse, boots and a dark curly hair. Next, the two women walking towards the camera. Notice the blonde one on the left with the pony tails, dark jacket with the multi colored cloth at the bottom, and grey pants. Fast forward to when the taxi pulls up to take Sherlock and Watson to the the crime scene. As Sherlock opens the taxi door, the same first lady with the curly hair and the blonde with the ponytail are now walking together in the same direction the blonde was walking when Sherlock arrived. (00:12:58 - 00:17:51)
Continuity mistake: Early in the episode Sherlock and Dr. Watson enter a cab in daylight for a ride to the crime scene in Brixton, which is a part of greater London. It is night when they arrive.
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.
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.
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.
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.
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: 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)