Fans who haven't got a long history with the character might wonder what, exactly, is going on here and even the comic book fandom can't possibly be hoped to anticipate everything considering that Webb hasn't been shy about changing little things to make the film fit his view of the series more clearly.
So--what do we want to know, coming out of our screening of The Amazing Spider-Man?
What happened to the guy who shot Uncle Ben?
It was the major driving force of Spider-Man's early career, but once he got some sense shaken into him by Captain Stacy, who pointed out that pursuing a personal agenda wasn't particularly heroic or honorable, the plot thread disappeared completely as Peter grew into the Spider-Man fans expect. That leaves Uncle Ben's killer out there at large, though!
It's one thing for Batman never to have found his parents' killer in the post-Crisis on Infinite Earths iteration of the character's origin. Some random dude who you didn't get to see for long at a time when you were presumably cowering for your own safety. Spider-Man, though, knows exactly what the guy looks like, and has powers already by the time it happens.
It's not just an idle question, either; the new Spider-Man universe seems to be one where there's an interconnected web (forgive the pun) of conspiracy that involves Oscorp, Peter's family and more--and Ben and May certainly know more about it than they let on. Would it be totally implausible to assume there's something larger at play, and that the mugger may have been sent into that neighborhood with a design on Ben to begin with? Certainly it would explain why Ben tried to get the gun, if he recognized the man.
What's wrong with Norman Osborn?
"He's dying," we're told early and often in the film, but we don't really know exactly what it is that the billionaire is suffering from, other than a case of Spider-Man coming in and messing his plans.
Whatever is wrong with Osborn, it's a major part of the plot, as at least Connors and possibly even Richard Parker have been working diligently to cure it for some time, with no real results. It's clear their genetic research is key to his recovery, and that he won't take "no," or even "I can't," for an answer.
Parkinson's is a distinct possibility as it's not only mentioned in-dialogue (though not in any way associated with Osborn) but we see a mysterious man with shaky hands at the end of the film who it's implied may be our first on-screen look at the man who would be Green Goblin.
How many people know who Spider-Man is?
One movie into the series and he's already got half of New York knowing who he is. Granted, it was impossible (or near-impossible) to avoid certain people finding out who's under the mask, but it seems as though there are as many people who know he's Spider-Man by the end of the film as there are surviving supporting cast members.
This makes Bruce Wayne's "unmasking to every hot blonde I meet" habit from the '80s and '90s films seem downright secretive by comparison.
But even beyond the named characters we can readily identify, there were a handful of police officers who heard him identified by name at the scene of his showdown with Captain Stacy's troops, and there had to be at least a few students at his school who noticed him moving in the other direction when people were evacuating. His wounds from the Spider-Man/Lizard battle might be explainable by "a piece of the school fell on me," but that would take a lack of common sense that most of the characters in this film didn't have. Actually, as much as it's easy to be critical of so many people figuring out the secret identity so fast, it's nice to see characters in a superhero movie that are smart enough to see what's right in front of them.
What "really" happened to Peter's parents?
The Amazing Spider-Man was marketed in its earliest days as "the untold story," and a key part of that is the plot involving Peter's parents, Richard and Mary Parker.
It's unclear whether they're actually dead, because even though it's strongly implied that they are, there's a throwaway reference at the end of the film, asking Connors if he told Peter what really happened to them. But even if they really are dead, it's clear their "accident" was anything but and that there's more to the lives and deaths of Richard and Mary Parker than meets the eye.
Whether Peter himself is somehow tied up in all of its is an interesting question, as well: a line that appeared in a number of ads and trailers but which didn't appear in the film featured The Lizard asking Spider-Man something like, "Do you know who you really are?" That, coupled with Peter's easy mastery of a profoundly complex equation that had stumped his father and Connors for years, lends a little credibility to the suggestion that Peter might be more deeply entrenched in whatever happened to his parents than he thinks.
Who was Connors talking to during the credits?
This is, of course, the one that most people are going to say, "Well, duh!" Because it was clearly implied to be Norman Osborn.
That said, Curt Connors and The Lizard had at least one scene of a Gollum-like, talking-to-myself monologue, and since he's locked up when the conversation happens and the person he's talking to disappears seemingly without the door ever opening, the possibility that he's hallucinating the whole thing can't be ignored. Even if he is, though, the suggestion is that whoever he's talking to is a dangerous person who knows a lot of the answers to these other questions.