Although Selma wants to take care of a child in this episode, she had earlier decided not to bother with kids after trouble with Bart and Lisa in Selma's Choice. However, she might have changed her mind at some point.
This is the second episode where a panda attacks Homer. The first was Homer vs. Dignity (only in this episode, the panda doesn't sexually assault him).
This episode has been banned from China (much like "Thirty Minutes Over Tokyo" was banned in Japan and "Blame It on Lisa" was banned in Brazil) for the unflattering references to the country, including the scene of Homer saying that Mao Zedong was "like a little angel that killed 50 million people."
Dana Gould was in the middle of adopting a daughter from China when this episode was made. Fearing the episode's content might have a negative effect on the process, Gould was credited as "Lawrence Talbot" (the name was taken from The Wolf Man).
When Selma says the car is too hot, Burns says it is actually cooler than Guy Lombardo, a famous Canadian band leader.
Mr. Burns says his car once outraced the Flying Finn, Paavo Nurmi, an athlete who won 9 Gold Medals at the 1920, 1924 and 1928 Summer Olympics. Both this and the afore mentioned references are among the many Burns age jokes that have been used throughout the series.
The dragons Homer imagines are white, gold, and red, but at the end the white one is green. That first dragon also resembles the one who appears in Spirited Away.
The Simpsons watch a bad performance of Death of a Salesman with a dragon in the back that has 'American dream' written on it.
The title of this episode is a pun on moo goo gai pan, the name of a popular pseudo-Chinese American recipe, based on the Cantonese dish mah gu gai pin, which is composed of fresh button mushrooms and other vegetables with sliced chicken. "Goo goo" is what babies say.
China (except for Hong Kong and Macao) uses the Simplified Chinese characters, but many signs in this episode are clearly using Traditional Chinese. However, there are still signs that use Traditional Characters in China.
The correct spelling of the place would be "Tian An Men", not "Tien An Men" (as this is the Wade system).
When Selma stands in front of the tank piloted by Wu, the shot is highly reminiscent of the famous image of the Unknown Rebel (dubbed in the international press as the "Tank Man") blocking the line of tanks during the Tiananmen Square protests.
While flying to China, the plane passes over a monument to "Warrior and spicy chicken pioneer" General Zuo Zongtang.
Lisa mentions the Great Wall of China was built to repel invaders, though historically it was unsuccessful.
The original broadcast portrayed the body of Mao Zedong covered by the flag of the Communist Party of China with the hammer and sickle (as is the case in the actual mausoleum). Later broadcasts of the episode has the flag substituted for the Flag of the People's Republic of China.
In the Chinese consulate there is a map behind the consulate official showing Taiwan as a separate country, extremely unlikely given the PRC's position regarding Taiwan (Republic of China).
There is a plaque reading, "On this spot in 1989, nothing happened", in Tiananmen Square, a reference to the Chinese Government's denial of the 1989 Tiananmen Square massacre. It is also a reference to the year The Simpsons first aired.
In addition to being a sardonic reference to the massacre, the sign in the square ("On this site in 1989, nothing happened") is a parody of real signs. Available from catalogues, they are mock-historical plaques that say: "On this site in 1897, nothing happened."
What's written on the adoption paper is gibberish, not Chinese, though this may be a play on the fact that computers which do not have Chinese text support installed may transcribe gibberish and random symbols in its place (mojibake).
The Simpsons leave on a Junk from Hong Kong, as evident from the background.