In the final scene, first the breathing tube next to Cpt. Gregson was not connected, but once they cut to London and back the tube is connected.
A car number plate ZM38 JNX is seen as the moped rider arrives outside 221B. This would mean that the car is actually from the year 2038 under the UK's vehicle registration system (and no current number plates start with a Z, as the first letter determines the region the vehicle was registered in).
At 42:02, when Sherlock removes the phone from his ears, it automatically goes to the speaker.
Around 20minutes, Sherlock talks to Kitty in London. Behind Sherlock is an American swinging yellow traffic light. London traffic lights aren't Yellow or suspended like American ones.
When DCI Jones is talking about the tabloid coverage of Lola Quinn with Sherlock and Joan, there is a shot of the police report. The crime took place in the Borough of Southwark, but the county is listed as "City of London". The London Borough of Southwark is part of Greater London, which is separate from the historic City of London.