In the very last shot of the film where Brandon looks at the woman on the subway train, the subway ad of a church called The River NYC is prominently featured behind him. This is actually the church Carey Mulligan attends whenever she is in New York City.
The scene where Brandon hears his sister sing in the restaurant was shot in real time. James Badge Dale and Michael Fassbender had never heard Carey Mulligan sing before so their reactions were real. The scene was shot at 3 a.m with cameras focused on all 3 performers at the same time.
During the 2012 Newsweek Magazine Oscar roundtable, Michael Fassbender said that he really urinated on camera during a scene in which his character was seen urinating (usually these sorts of bodily function scenes are simulated during the filming of a movie, if only because of the difficulty of replicating them over multiple takes). George Clooney, who was also participating in the roundtable, asked Fassbender how many takes he had to do of the urination, and Fassbender said three.
During the jogging scene, Brandon is seen waiting at a stop light and in the background is an advertisement for the TV series Army Wives (2007). Lucy Walters, who plays the woman on the subway train, also appears in Army Wives as Amy Sandberg.
The trivia item below may give away important plot points.
The sex scene with Michael Fassbender and Amy Hargreaves pressed against the glass of a room window in Manhattan's The Standard hotel was actually filmed above a busy street during the day. Spectators watched while the two actors, in the nude, smiled and waved at them from the hotel room above between takes. Since the Standard Hotel opened in New York in 2009, it has become notorious for its guests engaging in public sexual activity in front of their rooms' windows, sometimes for the entertainment of audiences on the street or in the High Line park below the building. This phenomenon has been documented in articles in New York Magazine, The New York Post, and The Observer, among other publications. In 2013, a Chinese couple fell to their deaths while reenacting this scene, when the window they were leaning against gave way.