Continuity mistake: When Moriarty puts the gum on the glass case around the crown jewels, the gum moves between shots.
Plot hole: For the supposed code that hacks into UK system, Sherlock deduces that the finger taps are counted as 1s in the binary code and the rest (while Moriarty's fingers are in the air) are taken as 0s. Sherlock can't know the rate at which the rests are counted in the binary code that he thinks Moriarty tapped out. So even if the key code was real, he wouldn't have known what it was.
Suggested correction: I think you could figure it out, assuming the rests are all approximately the same length, which is also similar to the tap length, which is how most people would intuitively try to tap a binary code. As there can only be whole numbers of 0s, there can't be that many possibilities for the code. Also, if Moriarty wanted Sherlock to find the code, he would have taken care to make it deducible.
Continuity mistake: When John shouts Sherlock's name just before he jumps, he lowers his phone away from his ear. He does the same thing again when he sees Sherlock falling.
Factual error: Some information about glycerol is displayed. The information is correct except for the structure of glycerol, which does not match the other information. Included in the information are "1,2,3-triol" and "3 hydroxyl (OH) functional groups." Both of these bits of information indicate that the molecule has 3 (OH) groups; however, only two are shown in the structure (conveniently coloured red). The red "OE" should also be an OH. (There are additional errors in naming, which are excusable here.) (00:00:37)
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.
