Revealing mistake: At the beginning, when Ivan and the two New York businessmen approach the school, the three are seen through a window from inside the school. If you pay close attention to the reflection of the students in the window, you can see that they are in no way doing anything related to what is being heard inside the school. After the class is dismissed and starts to leave, we see Ivan and the two businessmen begin to enter the school, and if you look in the window, the class is still going hard.
Factual error: During the karate tournament towards the end of the movie if you'll notice the American flags in the background you'll see that they are displayed improperly. Whether flags are being displayed horizontally or vertically, the stars should always be on the left side of the flag.