Character mistake: They are in the interrogation room questioning the fiancé of the scientist Natasha when the captain says, "the blood we found at the scene of your fiance's murder, it didn't belong to Bobby Cordero." The characters name was Benny Cordero, which the captain says correctly a few lines later. (00:33:25)
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.
Character mistake: Sherlock states that Sean Figueroa has "such blue eyes" even though he has brown eyes. (00:39:05)
Character mistake: The number of victims of the balloon man changes from seven to eight between the initial scene where he is introduced and where Holmes finds out the identity of the original balloon man.
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 ★