When Casey and Namiko go onto the train, the medallion hoodie is following them outside. Just before he stops, a red metal pillar is visible. In the next scene, there is no red metal pillar.
in the fight on top of the police station, Masazuka strikes above Casey's head, causing a very visible white scar on the wall behind Casey. In the next scene of the wall, the scar is gone.
As Casey and Namiko flee from the Professor's house following the attack, Casey jumps over the oncoming car, landing approximately 2 meters behind it. When the driver gets out of the car Casey is standing at kicking distance from him.
At 54:05, Namiko has her back pressed against a wall, cornered by Masazuka. Her hoodie is halfway down her arm, exposing her shoulder. In the very next shot, her hoodie is suddenly covering her shoulders.
Masazuka faces Casey during their first fight with his bokken in his right hand. This is not correct form when facing an opponent as it precludes rapid drawing of the weapon and striking. The students (including Masazuka) sit correctly at the start of this sequence with the weapon on their right hand side to signal that they do not have hostile intent, whereas Masazuka keeps his weapon in his right hand after rising. This is evident when he must rapidly shift hands before the fight begins.