While You Were Sleeping - S1-E2
Other mistake: When Sherlock was slapped, he later says he was surprised because the girl who slapped him was a "lefty." Then he rubs his right cheek and says it's leathery from all the slaps he's gotten, while the left is soft. This is backwards - anyone hitting him with their right hand would hit his left cheek.
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.