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.
Character mistake: Lestrade mentions that there could be some "poor sod covered with semtex on the streets somewhere" when talking about Moriarty's victims, but semtex does not go off via gunshot, much like C4. But that is what happens when one of the victims dies however, so the explosives are not semtex.
Suggested correction: The term "Semtex" is often used to refer to any plastic explosives, much like the term "Hoover" for a vacuum cleaner or "Kleenex" for a tissue.
But that doesn't negate the mistake.
Other mistake: Watson never orders, but somehow while in Angelo's, he has a full plate of pasta.
Suggested correction: Angelo feels so grateful because Sherlock saved him once that he immediately puts out food for him and his friend without being asked and without charging, in a 'here, have some' way.
