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: When you see Sherlock and Watson in the museum, Sherlock leaves and nearly gets shot. You see him dive behind the large statue, which moves. That's unusual for a large statue, but looking closer, you can see there are wheels attached to the base. (00:49:35)