The guard that Alex stabs in the hand with a pencil late in the movie is the same actor that played Burt who got in the bar fight with Travis in the first movie.
The form that the children do at the beginning of the movie is Koryo, the first form learned in WTF Tae Kwon Do as a black belt, although many schools teach it sooner.
In the arena, Tommy Lee does a cartwheel kick against the Russian fighter with his front side to the camera. In the next shot the kick is still in motion, but with his back side to the camera.
During the gun fight scene at Grandma's ranch James get shot by one of the gunmen and his left little finger and left ring finger are blown off. In the next couple scenes when he's shot by other gun men you can see that his left hand is fully intact with his little finger and ring finger still attached. When James crawls across the car to stab one of the gunmen his little finger and ring finger are missing like they should be.
When Alex and Tommy go to the Coliseum to search for Travis, and they question Weldon, he says the Coliseum is a dance club, period. Alex responds "Travis Brickley doesn't dance." Travis did plenty of dancing in Best of the Best.
What are the differences between the theatrical version and the unrated version?
A
The US-DVD, despite being labeled "R-Rated", features the unrated version of the movie. There are some differences in comparison to the censored R-rated version, though.
A detailed comparison between both versions can be found here.