In one of the training scenes early on in the movie, Virgil throws a flying kick at a speedbag. He turns around, and his beard is shaved. The next time Virgil appears, he has his beard again. In the timeline of events, he does not officially shave his beard until right before the team leaves for Korea, near the end of the movie.
During the match between Alex and Sae Jin Kwon, when both teams rush to the stage, Dae Han when he jumps on the stage in wearing sneakers. When Dae Han runs to break up Alex and Kwon, Dae Han is wearing Shin Instep guards instead of the sneakers.
When Tommy & Travis are sparring in the ring, Tommy pulls a punch when Travis is on the mat. In the wide view, Tommy is punching with his left. In the closeup of Travis immediately after, Tommy's right fist is in the shot above Travis' face.
When the fighters are holding the pressure pad for each other and Tommy kicks Virgil during this training session and sends Virgil flying to the ground, the black crash mat that he lands on to cushion his fall is visible, but when everybody rushes to see if Virgil is OK the crash mat has vanished.
When Alex receives his letter indicating he has been selected for the National Team, the word Congratulations is misspelled as "congradulations".
After Mr. Lee receives a letter during Karate class, the camera cuts to a close-up of the letter in which the word "Congratulations" is spelt "Congradulations."
When you see a shot of the Koreans training in a temple there is a sign whose characters are clearly Chinese. (Korean characters do not look anything like Chinese ones.)