After Sherlock comes back from Barts, he tilts the door knocker to the right before entering the flat. When they come back down to leave the flat after Magnussen's visit, Watson pulls the door shut holding the knocker and, when he leaves it, it is now tilted to the left, but in the last frame in that scene just when Sherlock's taxi leaves, the knocker is straight again.
When Magnussen is scanning the group at the Parliamentary meeting, the text on the screen identifies Lady Smallwood's first name as Alicia. In all further references, her first name is Elizabeth.
The helicopter that Sherlock and John use to go to Magnussen's house is the same (same registry number) that Mycroft uses when the Police raids the house.
Holmes "corrupts" the magnetic strip on his stolen key-card by pressing it against his cell phone but then he does not swipe the card through a slot. He presses it against a touchscreen display. That means it is not a magnetic key-card but one with an RFID chip. Microchips are not even theoretically corrupted by magnets like those in cell phone speakers because they do not rely on magnetism to function or store data.
As proven by Mythbusters, cell phones do not corrupt magnet strips on key-cards.
When Charles Magnussen told Sherlock that he'd been "reading" and that there's "rather a lot," the pressure points are only scrolling through 6 different pressure points multiple times. However, 6 pressure points is still a high number compared to the others.
When Sherlock is falling back after being shot the camera angle tilts and at the same time you see a plant in the background that's on the floor. It begins to slide at the tilt. This was intentional (see trivia).
When Sherlock falls to his back, some kind of support beams appear visible behind his shoe heels.
Set on Christmas Day in the UK, every tree is in full leaf.
At 1:10:06, when Watson and Sherlock are heading over to the helicopter, a man with dark, straight, short hair and a black/dark blue jacket is shown walking towards to the helicopter. Watson has brown hair and is in a brown jacket and Sherlock is in his overcoat and has curly hair. Who is this mysterious character?
Mrs. Hudson says behind the face of Big Ben. Big ben is the big bell in the clock tower. It is neither the clock nor the tower.
When Mary is walking down Leinster Gardens there is a signpost which shows Leinster Terrace behind her and the sign for Leinster Gardens is wrongly pointing to her right. In fact Leinster Gardens and Leinster Terrace form 1 continuous road, so she was indeed walking down Leinster Gardens.
Holmes claims that none of Magnussen's gigantic library of kompromat is stored on computers because those can be hacked, but all of it was stored as "hardcopy". That cannot be true though because he has all sorts of data about people he sees displayed on his VR glasses all the time. That would of course not be possibly if it were not stored on computers.