Continuity mistake: When the karate kid first goes to Mr Han's house to train, he drops his jacket by the doorway. Later on as they are talking, you can see his jacket move to different spots on the ground between shots.
Continuity mistake: When Dre is looking through the wood posts at the lady who is "mind controlling" the cobra, in the exterior shots of the window there are 4 bars, but in the interior shots there are 7 bars.
Continuity mistake: Dre visits Han when he is smashing his car, and Han sits in the driver's seat; Dre sees the paper clip on the hood - the paper moves several times during the shots. From having a quite amount of glass on it, to no glass, to a little glass. And it switches positions three times.
Continuity mistake: After Han told Dre about his family, and Dre gets the sticks to let Han train him. During several shots, the rope on the sticks switches several times from being on and off Han's hands.
Continuity mistake: When Dre and Sherry leave the US for China, the number on the plane changes from B-2460 to B-2443. (00:04:55 - 00:05:55)
Continuity mistake: When Dre is spying on Cheng and his friends from behind a moving car Dre's hand moves from in the door to beside the door between shots.
Continuity mistake: In the end when Dre is finishing Cheng, you see that Cheng switches positions - from being close to Dre, he is a little bit farther away.(Just to avoid getting hit for real).
Continuity mistake: When Dre pokes his head through the bars to see the lady with the cobra, you can one of the bars is bent enough for him to do so. Now when they switch to the interior scene he's looking at her from the inside but the bars are straight. (01:19:50)
Continuity mistake: In the scene where Master Li looks at his students bowing to Mr. Han, he is standing up in the crowd and a few moments later he is on the floor behind Mr. Han and Dre when they do their fist bump. In the alternate ending he was on the floor because he was beaten by Mr. Han in a battle, but in the original scene he just randomly appears on the ground. (02:01:20)
Continuity mistake: When Dre and Mei Ying are in the cafeteria for the first time, Dre puts his chopsticks in the small slot on the side of his tray. The angle changes to a front view of him setting his tray on the counter for lunch ladies and he puts his chopsticks on the tray a second time, now horizontally across the tray.
Answer: Because Dre has finally earned Chengs respect. The other Fighting Dragons bowed to Mr. Han because in China bowing is shown as a sign of respect as they see that he is a better teacher and a kinder master then Master Li.
Since this movie mirrors the 1984 original movie, this is like how Johnny Lawrence (William Zabka) and the Cobra Kai's (excluding Dutch [Chad McQueen]) finally respect Daniel Larusso (Ralph Macchio), after the latter defeats Lawrence-The only difference is that the Cobras do not bow to Mr. Miyagi.