Plot hole: The movie takes place before and around 1938 and, supposedly ends in that year, following the entrance in Shanghai of the Japanese, with the exodus by many Chinese and foreign residents. Ralph Fiennes' character, as an American ex-diplomat and businessman, would have resided, have bank accounts, his car, etcetera, in the foreign concessions. The Japanese did not occupy the concessions until after Pearl Harbor, so there was no need for him to flee the city, as a refugee without a passport and with little or no money, sailing towards Macao in a fragile Chinese junk. He could just have driven or walked a few blocks to any of the "Western" concessions, from where he could have married Natasha Richardson's character, obtained U.S. passports (White Russians had none, as the rest of her family in the movie until assisted by an official in the French Consulate) for her and her daughter, purchased a ticket in a safer vessel, sold his assets (regardless of the damage to his club, he still had a house, furniture, a car, presumably bank accounts, etc.).
Plot hole: When Pumpkin is telling Sayuri about Hatsumomo talking to Dr. Crab, she says that she was waiting outside during the conversation, and while she could hear it, she couldn't see them. However, at one point Pumpkin describes a facial expression of Dr. Crab.