Okay, for what I would want in the sequel (besides a better constructed script) or rather what Im imagining could happen in the sequel could be the following:
First, since this trilogy is supposed to have the disappearance of Peters parents be the driving mystery, the film can open with another flashback to them that sheds further light on why they had to leave Peter behind. Then the film can open with an action set piece showing Spidey fighting The Shocker and his gang committing an armed robbery. And of course, the question would arise as to where the Shocker got such technology (its from Oscorp obviously).
If the Amazing Spider-Man video game is canonical, then this film will take place during the fall in which Peter starts his Freshman year at Empire State University, along with Gwen. Its there he meets Harry Osborn, who is Gwens long-time childhood friend, which makes Peter a bit jealous. Which also means that Norman Osborn gets be introduced as well, as Harry is at his beck and call, feeling as though hes treated more like a servant than his son. However, but he should still be kept hidden for the most part until towards the end of the first act; we just hear his voice and see his hands, but can tell hes gravely ill under the care of Dr. Otto Octavious. And yet, when he decides to make a public appearance at an Oscorp benefit after years of seclusion, he appears perfectly fine and healthy. This will be an ongoing mystery in the film until a pivotal moment where pivotal Spidey decides to confront Osborn at his home. Oh, and it also gets established that Osborn is rather unhealthy obsession for Gwen, which is part of his desire to become young, strong, and healthy once more and, of course, be key later on.
However, Osborn isnt the main villain, at least not directly. That would be Mysterio, who gets revealed as The Man in Shadows from the end credits. His debut can take place during the same Oscorp benefit, allowing for Spidey first fight him and his "Enforcers" in which, of course, he loses as Mysterio is able to get away. Then, afterwards, Mysterios gimmick will be to announce his crimes beforehand on television and internet broadcasts challenging Spider-Man to stop him. And his tech is so advanced it seems like real magic. This can allow for some action set-pieces such as Coney Island in homage to Amazing Spider-Man #67-68, a rotating room a la Amazing Spider-Man #24, hallucinations of Uncle Ben, his parents, and Captain Stacy, etc.
In terms of subplots, Peter can learn that, because of Uncle Bens death, Aunt May doesnt have enough to finish paying the mortgage on the house, which forces Peter to look for a job. Thus leading into the Daily Bugle and J. Jonah Jameson. In this version, he and Captain Stacy were good friends, and, ironically, he initially saw Spidey as a hero until Stacys death. Now he blames Spidey for failing to save Stacy and is taking up his friends crusade by attempting to turn public opinion against him.
Another is the introduction of Mary Jane Watson (including her classic entrance) in which shes just moved in next door to live with Mays friend, Anna. MJ appears to be a happy-go-lucky girl, but deep down shes angry because of her parents divorce and has a rebellious, undisciplined streak, pretty much how Gwen Stacy was depicted in the Ultimate Spider-Man comics. If Gwen reflects Peters intellectual, scientific side of his personality, MJ reflects anger at feeling abandoned and non-conformity. Basically, Peter helps to prevent her from going down the wrong path like he almost did in the first film. Which is key for the end of the film in that she returns the favor in a way that should be apparent.
Anyway, when Spidey next time faces Mysterio, the villain states he has a hostage who will die that Spidey must save. And it turns out the hostage is Uncle Bens killer, thus giving Peter a choice as to whether or not to take his revenge. Spidey, however, saves him, but Mysterio kills Uncle Bens killer and Spidey is captured and taken to Osborn.
Because of this, several things get revealed: Mysterio is not only Osborns right-hand man, but was part been an elaborate test of Spider-Mans abilities for the purposes of determining whether or not his DNA will be a viable cure for Osborns illness; the same goes for the Shocker at the beginning of the film and, perhaps, other Spidey villains that are referenced. Second, that the healthy Osborn is revealed to be a Life-Model Decoy provided by Mysterio, and the real Osborn we see looks like someone undergoing chemo-therapy and forced to walk on canes. Third, that Osborn has been known Peter was Spidey since day one, as he has tapped into every security camera and cellphone in the city--including the biocable lab at Oscorp and the convenience store where Peter allowed to let the robber go. And finally, Osborn reveals the truth about Peters parents and why Peter is the only successful cross-species.
Spidey is then forced to donate his blood to create a serum for Osborn and the scene plays out very much like how Osborn became the Green Goblin in the Ultimate Spider-Man comics, with things appearing to go well before something goes wrong and the lab explodes (and hints to the creation of Doc Ock in the process). This also leads to Osborn (very much like how the Goblin was in the Ultimate comics) kidnapping Gwen and leading into a scenario not unlike The Night Gwen Stacy Died. Thus by the end of the film, Gwen is dead, Spidey is blamed for the murder of Uncle Ben's killer, Gwen, AND Norman Osborn. We also get a scene reminiscient of what happens at the end of "The Night Gwen Stacy Died" in which MJ decides to stay and comfort Peter in his grief.
