During interrogation Kuze removes half of Major's robotic face, and her hair falls over the exposed left eyeball. He then replaces the half-face without first brushing this hair out of the way, yet in the next shot she looks perfectly normal.
When Cutter confronts Aramaki in his office from across the desk, Cutter's hands don't match. When the camera is behind Cutter, his hands are balled up and he is leaning on the desk on his knuckles. When the camera is behind Aramaki, Cutter's hands are flat and he is leaning on the desk with his fingers straight.
When Major visits who she suspects is her Mother, and they sit down at the table for tea; with each character's point of view to the other switch, the tea pot handle is up (from Major's view) but then down from her reverse (Mother's view) shot: and the kettle that boils the water whistles its ready - yet has now whistle attachment to its spout.
When Major meets Motoko's mother for the first time, she puts the kettle on the stove to make tea and it whistles. However, the kettle on the stove is not the whistling kind, which has a distinctive spout.
In the car and suitcase shooting scene, Aramaki somehow manages to fire 8 shots out of a 6-shot revolver without reloading. That his revolver only holds the (typical) number of 6 cartridges is clearly visible in a close-up in previous scene.
When Major shoots the geisha robot in the face, the robot's face is open, revealing its inner workings. The face then closes and, when next seen, the impact patterns from the bullets smoothly cross the seams of the closed face which they would not do if the face were shot when open.