Goofs

The car underneath the spider tank changes in size relative to the tank between shots.

During the opening assassination scene, Nakamura gets blood splattered on his face and suit. As he approaches the window in the following shots, the blood is no longer there.

Before Kusanagi leaps off of the building in the opening, she is wearing black gloves and black boots. In the next shot, she is suddenly wearing white gloves and white boots, both of which seemingly came from nowhere.

In the opening of the film, the officers have "POLICE" printed on their uniforms in white with a black outside stroke. For the rest of the movie, the text is printed in just plain black text.

In the third act of the film, when Batou rams his car into the decoy car, the animators didn't draw the license plate on the back, as it was seen in previous shots.

Director Mamoru Oshii went to great lengths to portray gunfight scenes accurately, yet during the foot chase in the market the terrorist fires armour piercing ammunition wildly through the crowds and apparently hits no one. No collateral damage was seen or shown which stretches belief.

During the montage through the city, where there's an ally way in a shopping district, one character is drawn small to appear as though they are inside a building in the distance. However, the character is layered over a doorway rather than behind it, making it appear as though he's very small.

Sometimes considered continuity errors, but in reality just animation layer changes. In the early days of cell animation in Japan (hence anime) the parts of the scene that 'moved' or were animated, are layered on background stills that were static. The animation cells could be noticed as being 'brighter' and had less complicated shading or artwork applied. Thus, for instance, doors or objects that move would appear slightly different than the background artwork a 'moment' ago or later. A different technique is used for character movement to take into consideration perspective shortening/lengthening.

In the shot where Motoko jumps off the building and uses her therm-optic camouflage, there are numerous cars behind her that clip over the bridges they aren't supposed to be driving on, along with cars that disappear and reappear within the same shot.

When we see the minister's interpreter connected to some kind of equipment, the display on the equipment in the background can be seen clipping over wires and tubes in the foreground.