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.
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)
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.
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.