At 12 minutes into the movie after missing her target at night in Tokyo Kate runs through the rooftops and after a roll her hood falls back. She then slides behind something very briefly and appears close to the camera with her hood again on her head.
The film begins with Kate and V in the Vanilla truck preparing for a "hit," her hair parted to the LEFT. Her hair is then parted to the RIGHT once she is in position to execute.
After stealing the medication from the Doctor at gunpoint, Kate exits the hospital and looks for a unlocked car. Upon Finding one, the scene skips what would be the car starting up. The Japanese society is very secure about their property. You are lucky to find one unlocked, exponentially that much more lucky to find one with keys in the car as well.
Kate is poisoned by Polonium-204, which the movie seems to suggest is more deadly than Polonium-210 (the more common isotope), but this is wrong. Polonium-210 is an alpha-particle emitter, while Polonium-204 is a beta emitter. Alpha particles (helium nuclei) are far more destructive inside the human body than beta particles (electrons). Kate would probably have survived Polonium-204 poisoning, but not Polonium-210.
Kate tells the doctor she kidnaps at gunpoint that the gun is pointed at his femoral artery, but the gun is pointed at his abdomen at the height of his external iliac artery. She then states that the heart pumps two litres of blood a minute, but a human not under duress has a cardiac stroke volume of 5-6 litres per minute.
Before Kate goes to kill Verrick, her gun is empty, and she puts in one bullet. After she shoots him, the slide on the gun is not in the locked back empty position.
When Kajima stabs Renji, the sword emerges from his chest without blood.
In conversation, both Kate and Ani refer to Ani's uncle by his surname, Kijima. But as his brother's child Ani would have the same surname, so it's as if she is talking about herself.