These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Batou: "If it looks like you've gone in too deep I'm pulling the plug and taking you home!"
Adaptation Displacement: The first film is far better known than the manga it's based on, particularly in the West where it really took off. Today's generation of anime fans, however, seem to be more familiar with Stand Alone Complex than either the films or the manga.
The lesbian sex scene in the original. Comes out of nowhere, is never brought up again in that book.
Man/Machine Interface had a sex scene involving a female African soldier getting gang-banged by 3 other soldiers. Shirow admitted to removing it from the North American release because it really added nothing to the story.
Designated Hero: While she's on the job, the Major is not a nice lady; at times, she seems to approach being a Sociopathic Hero. For example, in Section 9's first mission to determine if they would even be approved as an organization, Motoko ends up saving the lives of boys who were working in hellish totalitarian conditions and barely being fed. When they ask if she was here to help them, she told them that they have to make their own lives and not rely on hand-outs. Ouch.
And that's not even close to the worst thing she does.
Erection Rejection: A sizable faction of the fans maintains that Man/Machine Interface is unreadable because of this. The other faction maintains it is only readable because of that.
Everyone Is Jesus in Purgatory: The first movie can be interpreted as the Major leaving behind her attachments to her human existence and becoming a being of pure thought. The second movie's plot is more straightforward, but still contains lots of mind screwing.
Germans Love David Hasselhoff: In America, it's a bona fide classic. In Japan, it's considered to be average. In sales, not in quality. To Westerners it was one of the earlier examples of serious, artistic animation, while in Japan it was nothing unheard of and was, well, slow-paced and artistic; rarely a recipe for a box office hit.
Les Yay: The Puppet Master is referred to as "he," but is eventually seen in a female body and with (in the 2.0 remake) a female voice. And with all that talk with Kusanagi about "merging"...
Older fans of the movie tend to find the change of the Puppet Master's voice actor as one of the most unnecessary things in 2.0, as the original's use of a female body talking in a male voice was considered a masterful deliberate use of the Uncanny Valley.
Narm: The overabundance of philosophical quotes in Innocence could be seen as one. It's as if one of the writers brought home a book of famous quotes and was determined to have the characters recite every last one.
Paranoia Fuel: The possibility of having your brain hacked. In the second film, we get to see what the result of such hacking looks like from the point of view of the victim. It's rather unnerving.
Superlative Dubbing: The original anime film's English dub (courtesy of Manga Entertainment) was one of the very first anime dubs to aim directly at an adult audience, contain excellent acting all across the board and to have a script that was extremely faithful to the original Japanese with minimal use of extraneous profanity, a practice that was all too common back in the early-to-mid 90s, often used to supposedly make the product seem "edgier". The dub still holds up extraordinarily well today despite the many advances in dubbing courtesy of such shows like Cowboy Bebop, Fullmetal Alchemist and Gurren Lagann. It is so good that, in fact, when the remake Ghost in the Shell 2.0 was localized for English release, rather than create a new dub from scratch, the original 1995 English dub was reused wholesale with no changes. Now that is impressive.
Uncanny Valley: Both films play with this, especially Innocence with those eerie geisha robots, Haraway the forensics scientist, Kim and the really creepy-looking doll Togusa brings home to his daughter at the end. Discussed in Innocence:
"It's the uncertainty that perhaps something that appears to be alive actually isn't. On the other hand, it might be the uncertainty that what doesn't appear to be alive actually is."
Woolseyism: The English title is the subtitle of the original work. The actual Japanese title, Kokaku Kidoutai, translates to "Mobile Armored Tank Police". (Shirow Masamune mentions in the preface to Man/Machine Interface that the Japanese title is a huge misnomer for M/MI, because the story is no longer about the police, nor does the protagonist ride in an armored tank. He considered changing it, but...nah.)