As Sherlock and Mycroft describe a man on the street during their 'old game', the dialogue is taken practically word for word from Arthur Conan Doyle's short story 'The Greek Interpreter', which introduced Mycroft.
Holmes is shown reading "The Guardian" newspaper. In 1886 it would have been called "The Manchester Guardian". It didn't become "The Guardian" until 1959.
We are shown two newspaper front pages. The date of the first newspaper is Tuesday October 2, 1886. The actual day was Saturday 2nd. The second newspaper was dated Wednesday October 17, 1886. The actual day was Sunday 17th.