In the early drafts of the screenplay Greenberg was initially written as a guy in his early 30s. Inspired by the idea of casting Ben Stiller, Noah Baumbach and Jennifer Jason Leigh rewrote the entire script and made Greenberg 40 turning 41.
A poster of the band Prinzhorn Dance School can be seen on the wall where Greenberg hangs the drawing made by Florence' niece. It's a reference to LCD Soundsystem's James Murphy, who was responsible for the soundtrack. Murphy is the boss of the DFA record label, who released the 'Prinzhorn Dance School' album.
The trivia item below may give away important plot points.
The character of Florence (Greta Gerwig) bears some resemblance to the character Stacy Hamilton, played by Jennifer Jason Leigh, from Fast Times at Ridgemont High. Both are young, blonde women who are slightly overweight (by Hollywood's standards), who experiment with sexual promiscuity, and who fall into emotionally painful sexual relationships with much-older men. Both have abortions (a fairly rare occurrence in American movies and TV shows) and emerge relatively unscathed. Leigh, for whom Stacy Hamilton was a breakthrough role, both co-starred in and co-created the story for Greenberg.