When the gunman shoots the smoke alarm, his pistol has a silencer, but moments later as he points it at Dr. Watson, the silencer is gone.
The morning after the Christmas party, John is shown putting on his jacket while speaking to Mrs Hudson, then putting it on again as Mrs Hudson leaves the room.
When John comes in from the rain and tells Sherlock about Irene, the damp patches on his jacket come and go.
Near the end, when Mycroft is talking to Watson, he folds his hands and places his head on them. In the next shot, his hands are a couple of inches away from his face.
In the opening poolside scene, John's jacket containing the explosives is constantly seen in different positions.
When Sherlock and Mycroft go to identify a body at Barts Hospital, they enter a door marked "Morgue". Like most British hospitals, Barts has a Mortuary, not a Morgue which is a mainly American word.
When Watson, Holmes and Lestrade talk about the dead person in the car who had been supposed to be on the crashed airplane, Lestrade mentions that his passport was stamped in Berlin.
One can see that it is a UK passport, but European citizens' passports are never stamped when travelling within the EU and/or Schengen area, not even when leaving or entering.
When Sherlock leaves his apartment with the government guy who takes him to the airport to see the "Coventry" plane, a shot of Baker street in London (the street Sherlock's apartment is on) shows it as a two-way street. Baker street is a one-way street.
In the first paper - with the headline "Hat-man and Robin" - there are two paragraphs of text, and then parts of that text is repeated to fill in the page. Also, on one of the later editions we see, words from that first newspaper is repeated almost verbatim.
Although it is supposedly Christmas and New Year, the trees are all in full leaf.
The first time Watson is seen updating his blog, the text overhead progresses much faster than his typing - at a rate of roughly one word per key press.
Around 86 min in, John gives Sherlock the phone. When John reaches for it in the police bag, he grabs it in a way that would show the dial pad towards Sherlock. However, in the next shot, John places the phone in Sherlock's hand, with the dial pad facing John himself.
There is a typo on Irene Adler's website. It reads "Take the weight of your feet."
Near the end of the show, Sherlock Holmes is seen with his hands up high on the microscope, but when it changes views his hands are down lower.
(at around 40 mins) When Sherlock starts to play his violin after his conversation with his brother, the movements of the bow across the strings does not match the soundtrack.
(at around 42 mins) Reflection of crew is visible moving in the mirror on the wall behind and to the right of Mycroft.
Sherlock asks Mycroft "Why did you send John and I...?" The punctilious and precise Holmes would have used the grammatically correct phrase "send John and me".