Continuity mistake: The underground car seen in the CCTV video is from the Jubilee line, but is meant to be the District Line. It's also different from the one where the heroes defuse the bomb, which is an actual District Line train (D stock). The rounded doors is the most visible proof.
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)
Continuity mistake: We see John come into the room and stand next to Mrs. Hudson and put on his coat. After a few shots Mrs. Hudson walks away with the plates and says, "Lovely tune, Sherlock..." As she's walking away we see John isn't wearing his coat, and he puts it on again. (00:50:00)
Continuity mistake: As Sherlock and John approach the missing subway car, and especially as they bend to peer beneath it, the interior of the car to a distance of several feet is plainly visible through the window of the door (you can see the curved ceiling inside and some unlit fluorescent light bars). However, an interior shot then shows that there is a closed door inside the car, a foot or so inside the exterior door, that Sherlock has to push open to enter the car proper. This door should have blocked their view of the inside of the car before they entered. It didn't, so it has gone from open to closed between shots without anyone touching it. (01:05:35)
Continuity mistake: In the scene where Sherlock is on the roof of the hospital with Moriarty, when Moriarty shoots himself in the mouth, when the camera shot quickly changes from a close up and Sherlock moves back, the gun disappears from Moriarty's hand (to the right of Sherlock). In the next shot of him, it's still in his hand.
Continuity mistake: As Sherlock and Watson come out of their apartment to hail a taxi to be taken to Brixton and the scene of a murder, two extras can be seen in the shot - one crossing the road and one walking up the far side of the street. At the top of the street there are two white colored cars, but they suddenly disappear, to be replaced by a dark colored car. Also the light of the building across the road is suddenly turned on.