The article that Caden reads while in the doctor's waiting room, about his wife, is titled: "It's Good To Be Adele". The intro paragraph reads: "Six months ago, Adele was an under-appreciated housewife in Eastern New York. Stuck in a dead-end marriage to a slovenly ugly-face loser, Adele Lack had big dreams for her and her then four-year-old daughter, Olivia. That's when her paintings got small."
Philip Seymour Hoffman's character's last name is a reference to the Cotard delusion or Cotard's syndrome, also known as nihilistic or negation delusion, which is a rare neuropsychiatric disorder in which a person holds a delusional belief that he or she is dead, does not exist, is putrefying or has lost his/her blood or internal organs.
At the start of the film, when 'Phillip Seymour Hoffman' is reading the news at the breakfast table, he reads out that "Harold Pinter has died.... wait.... no - he's won the Nobel prize". This is a reference to a famous Sky News clip whereby Sky, in their rush to be first with breaking news, accidentally announced that Harold Pinter was dead. In fact it had just been announced that he was to be awarded the Nobel prize for literature.
The name next to the buzzer of Adele's apartment reads "Capgras." Given the subject of the film - a man has actors play the real people in his life - this is almost certainly a reference to a psychological phenomenon called the Capgras delusion, where the sufferer believes that everyone in his or her life has been replaced with an identical-looking impostor.
When Caden sees Hazel at the box-office, a brief shot reveals she is reading: page 1 of Marcel Proust's Swann's Way, the first book of his multi-volume novel Search of Lost Time. A recurring character throughout Proust's novel is Dr. Cottard, reportedly based somewhat on Proust's own father, a noted physician, and on the Cotard who gives the delusional syndrome its name.
Merriam-Webster's Online Dictionary defines "synecdoche" as: "a figure of speech by which a part is put for the whole (as fifty sail for fifty ships), the whole for a part (as society for high society), the species for the genus (as cutthroat for assassin), the genus for the species (as a creature for a man), or the name of the material for the thing made (as boards for stage)."
In the beginning Caden Cotard (Hoffman) is listening to the radio where an interview with a professor for Philosophy is playing. When she gives a bleak outlook on what life will become like, she is really citing a translation of the last paragraph of the seminal poem "Herbsttag" (Autumn Day) by famous German author and poet Rainer Maria Rilke, which, in its original language goes like this: Wer jetzt kein Haus hat, baut sich keines mehr. Wer jetzt allein ist, wird es lange bleiben, wird wachen, lesen, lange Briefe schreiben und wird in den Alleen hin und her unruhig wandern, wenn die Blätter treiben.