Ewan McGregor was uncomfortable about his parents watching the film, as he spends much of it being in the nude. His father took it well, and after seeing the film, responded to his son, via fax: "I'm glad you inherited one of my greatest attributes."
Much of the film is in Japanese, and some of the English subtitles appear to be intentionally incorrect or missing, in the spirit of "language play" or "the Tower of Babel". (Confirmed by director Peter Greenaway at a talk at the San Francisco Film Festival.)
The keeping of pillow books to record poems, secrets, and encounters with lovers was a common practice of noble women in Heian Japan. Although its content is unrelated to the film, a famous example was written by Sei Shonagon at about the same time as Lady Murasaki's The Tale of Genji which has the honor of being the world's first novel. In fact, it has been said that Sei Shonogon and Lady Murasaki were rivals in the court of Heian.
When Nagiko's mother delivers the birthday blessing, she starts in Japanese, as her father did, and then switches to Mandarin Chinese.