When Holmes is examining the sports newspaper in Jimmy's apartment, the basketball and baseball standings for each division in both conferences for both sports (12 divisions in total) are exactly the same.
At the end, Sherlock and Athena go out for dinner leaving a fire blazing in the fireplace. This is foolish in the extreme.
At the beginning of the episode, Joan tells Sherlock that "he seems annoyed with Harlan", she "noticed yesterday at the apartment"; however, it's still the same day as they just came back from Harlan's apartment and they are both wearing the same clothes, in fact Sherlock is just starting to create the case-board. He would not have waited a day to do this.
The FBI believes that Lily was kidnapped between the library and her apartment, that they say is a few blocks away, at 108th St and Amsterdam (Upper West Side); which is indeed close to the library at Columbia University where she is Harlan's student. Watson is to canvass that area, but she basically finds a witness on E 7th St, between 1st and 2nd Ave, 9 miles away in the East Village, the complete opposite area of Manhattan.