The article that Caden reads 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, Cotard, is a reference to the Cotard delusion or Cotard's syndrome, also known as nihilistic or negation delusion. It's a rare neuropsychiatric disorder in which a person believes that they are dead, do not exist, are decaying, or have lost their blood or internal organs.
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.
At the start of the film, when Philip Seymour Hoffman is reading the news at the breakfast table, he says "Harold Pinter has died. Wait, no, he's won the Nobel prize." This is a reference to a famous news broadcast in which Sky News, in their rush to be first with breaking news, accidentally announced that Harold Pinter was dead. In fact, he had just been selected to receive the Nobel prize for literature.
In a radio interview, director Charlie Kaufman revealed that while scouting for a location, he and a few other crew members became stuck in an elevator late at night and were afraid it would plummet. They had to open the doors and jump out to escape. In the same interview, Kaufman discussed a recurring and claustrophobic dream he has about being stuck in an elevator, and that the movie was purposefully structured like a dream (it has double the number of scenes than an average movie of its length).