Sherlock Holmes (Benedict Cumberbatch) has met his intellectual match in James "Jim" Moriarty (Andrew Scott).
Sherlock ends up solving another puzzle before the first casualties of the game occur. John and Sherlock are having dinner and sicussing the case, John suggesting that it could be Moriaty, the unkown boss of the killer cabbie in the first episode when Sherlock gets another call. The third hostage is a blind elderly woman, and unable to read from a pager, so the bomber must dictate to her the messages. Sherlock solves the case, though the hostage's vest is triggered once she starts to describe the Moriarty's voice. The explosion kills her as well as 11 of her neighbors, though it is staged to look like a gas leak, just like the one from earlier in the episode. Sherlock had encouraged the woman to tell him nothing about the man's voice, but she had continued, and Sherlock complains that he "lost that round" which angers John because it seems Sherlock is loving this challenge even though innocent lives are at stake.
John is subtly blaming Sherlock for those twelve deaths, though he had done everything in his power to stop them from happening. Sherlock tells John that Moriarty was protecting himself, and it is implied that he would have killed the old woman anyway, since she was the only hostage to have heard his voice. Sherlock solves another puzzle when a young boy's life is on the line with only a few seconds to spare, and ends up having to get involved in the case he gave to John. After they solve it, John is kidnapped by Moriarty and taken to the pool. Sherlock goes to rescue him, handing an important flash drive to Moriarty before he tosses it in the pool and tells Sherlock he could have gotten the information anywhere, but wanted to show Sherlock what he could do.
Much like Lady Macbeth is not reponsible for th death of Banquo, Sherlock is not responsible for the deaths of the 12 people. They had both done what they could to stop it, but the partis they were tying to stop would have done it anyway. Macbeth would have done it to protect his stolen crown, and Moriarty to protect himself from Sherlock for a bit longer.
Macbeth commisioned the murder of Banquo out of insanity, the death of Duncan having driven him crazy. Moriarty killed them because the old woman hadn't listened to him, and when Sherlock tells him that "people have died," Moriarty snaps and yells at him, "That's what people DO!"
Neither Sherlock nor Lady Macbeth should be blamed for those murders, as they had both been helpless to stop them. They were both dealing with insane men who could not have been told to stop, or even if they had been, would not listen and wuld continue on with their plans. Macbeth and Moriarty are similar in this way, that they will protect themselves at any cost.