A flag of Hong Kong Special Administrative Region is shown at the games of 88 in Seoul. The flag was first officially hoisted on 1 July 1997, in the handover ceremony marking the transfer of sovereignty.
The scene at the theater and Randy is doing his show. After he finishes his show and looks to audience, the man he eventually gives a heart attack begins to stand up. The camera switches to show people eating with a fart sound, and the man is sitting there eating. When the camera cuts back he is already standing up.
In the scene where Randy and Ernie first meet Maggie, Randy rushes in with a hat rack to assist in combat but ultimately is disarmed by Maggie. When she backs him into the corner, and he's shrieking like a scared girl scout, you can see his left hand knocks a picture off its hanger, though not onto the floor. The camera then cuts away from him for a time, but when it returns, you can see the picture is again hung up perfectly.
In the 1988 Olympic Games, Karl Wolfschtagg is shown wearing a uniform with the letters GDR, for German Democratic Republic, the official name for East Germany. In reality, East German athletes wore the letters DDR, for Deutsche Demokratische Republik (the name for East Germany in the German language).
In individual Olympic sports, competitors are identified by their names, not by their nations (as many individual sports would have multiple competitors from the same nation). Randy Daytona's and Karl Wolfschtagg's names would have appeared on the scoreboard, not "USA" and "GDR," respectively.
At the Olympics, a country would be identified with its official national name. "East Germany" would not have been used in official Olympic announcements. Karl Wolfschtagg would have been introduced as a competitor from the "German Democratic Republic."
When the Chinese guard asks to use the bathroom, the guard is speaking in Korean. This could've been deliberate because Feng speaks Chinese but not Korean; as he says "What?" after the guard finishes talking, as if he didn't understand him.
Rodriguez tells Randy that the Cantonese word "gweilo" means "round-eye." The literal translation is "white ghost" and it is most commonly translated as "foreign devil". However, this line is probably a joke.
When the Chinese Guard asks Feng to go to the restroom, Feng instructs him to the location of the restroom. However, if you look, he does not head towards the restroom, but returns to his seat which is off to the left. It's possible that he doesn't understand English (because he didn't speak English), so Feng's instructions make no sense to him. It's also possible that he didn't need to go to the bathroom, as he was speaking Korean, and the woman could have thought it was Chinese and translated it that way.