Character mistake: When looking at the car near the start, Sherlock says he can tell by the pattern of the bullet holes that the gun was fired in 3 round bursts. But when we saw the attack earlier, the gun fired in bursts of different lengths.
Continuity mistake: When Joan meets with her therapist, the nook behind Joan is brightly lit. The nook goes back and forth from brightly lit to very dark, sometimes in the space of a three-second cut to the therapist.
Chosen answer: M broke into the brownstone and left a note. Holmes deduced he was staying at a high-class hotel from the soap scent on the note, and gave a picture from a hidden camera to his "irregulars" on the street to stake out hotels. One of them saw him, so Holmes followed him to his next intended victim and knocked him unconscious with a baton.
Sierra1 ★