The map of China in the consul's office shows Taiwan in a different color than the mainland. The PRC government regards Taiwan as part of its territory and never does this on its official maps.
The plane on which the Simpsons fly to China has a 3+3 seat configuration, which is too small for a trans-Pacific flight.
The plot of the episode is centered around Selma using Homer as a fake husband to adopt a Chinese baby. However, she had a better solution living in her apartment. All she had to do was come up with a fake name for her sister and dress her up as a man. Since the baby would have Patty as a live-in aunt, it makes more sense to get used to Patty instead of Homer.