It's pretty common for movie trailers to include scenes that wind up not being in the final edit of the film. Amazing Spider-Man had a whole subplot about Peter Parker's DNA and the Lizard that was in the trailers but not the movie. And now, Amazing Spider-Man 2 also seems to have left out major scenes from the trailers.
In fact, a lot of stuff seems to have been left out of the second Marc Webb Spidey movie. Screen Rant reports there's a petition to release the "Director's Cut" of the movie, on DVD or in some other form. There's a theory that some scenes were cut for length, including some important character scenes.
So let's examine the evidence from the trailers. Here's what we know was shot and left out of the film.
More Norman Osborn
Sadly, Chris Cooper is barely in the movie, despite being an amazing actor and having spent all that time getting long fingernails glued on.
The trailers include this scene, where Norman appears to be telling Harry all about Richard Parker's experiments, and his son Peter's magic DNA. "What about Peter?" Harry asks. "Not everybody gets to have a happy ending," says Norman.
You have to assume that would change the whole shape of the film, if you had Harry knowing early on about Peter's spider-DNA stuff:
And in some of the trailers, you can hear a voiceover which is either Norman Osborne or Fiers (the mysterious figure who organizes the Sinister Six) saying, "We have big plans for you, Peter Parker."
And Movie Pilot reported on a rumor that there was a post-credits scene meant to be included in this film, after all — and it would have had to do with a photo that was released of a previously unseen part of OsCorp's evil basement:
Basically the post-credits scene is rumored to have involved Fiers coming into OsCorp's evil vault and finding the frozen head of Norman — then saying, "Wake up, old friend."
There's some speculation that Norman could join his son's team, the Sinister Six — but that this was cut from the end of the film because it was too soon to reveal that Norman was still alive. Or because plans changed.
More Harry Osborn
There seem to have been more scenes between Harry and Peter. Including the big one, which is in all the trailers, where Harry tells Peter that OsCorp had his family under surveilance. Why, Peter asks. "Isn't that the question of the day?" Harry responds.
There also seems to have been a bit more of the stuff where Peter and Harry are just hanging out. At least, I don't remember the exchange where Harry asks Peter what he's been doing, and Peter says "I've been doing some web design":
Also, there seems to have been a sequence where Harry, after becoming the Green Goblin, attacks OsCorp and runs into his old assistant Felicia:
A ton of the trailers include a long speech by Peter Parker, where he says that "The more people I try to save, the more enemies I will make. And it's just a matter of time before I face those with more power than I can overcome." There's also another version of it, in some of the later trailers, where he says "Every day I wake up knowing that no matter how many lives I protect, no matter how many people call me a hero, someone even more powerful could change everything."
More Gwen and Peter
And finally, there are a few snippets of extra Gwen/Peter stuff in the trailers, which is either alternate versions of what we saw on screen, or apparently extra stuff.
Like the exchange in the movie, where Peter shows up late for graduation and says he was held up — in the trailers, that same exchange takes place later in the film, when they're standing near the big Forever 21 store:
Also, Screen Rant noticed that the scene where Gwen tells Peter "This is bigger than you, Peter" doesn't seem to be in the movie:
Did we miss anything else? Honestly, of the stuff that was in the trailers, the most significant removal seems to be the stuff with Norman telling his son Harry about Peter, and then Harry telling Peter he was under surveillance.