Dr. Feld tells Kay (Meryl Streep) a metaphor about fixing a deviated septum, which Streep has in real life.
The French movie that Kate and Arnold see in the theater is Le Dîner de Cons (1998), which was remade as Dinner for Schmucks (2010) starring Steve Carell, who plays Dr. Feld.
According to David Frankel on the director's commentary, the MPAA was originally going to give the film an R rating due to the scene in the movie theater.
This movie marks the second collaboration between Meryl Streep and Tommy Lee Jones. They previously appeared together in A Prairie Home Companion (2006).