With all the comments about how this Spider-Man film shows Peter with mechanical webshooters, engages in witty banter and has Gwen Stacy as a love interest--thus implying this film will be more faithful to the comics than Sam Raimi's--there's something the trailer I think reveals should be a concern for die-hard Spider-Man fans.
Notice that the second trailer shows the scene with Peter having dinner with Gwen and her family just like the first trailer does? The dialogue shown in the first trailer that's repeated in the second trailer is as follows:
CAPTAIN STACY: So, tell us a little about yourself, Mr. Parker.
PETER PARKER: Not much to tell, really.
GWEN STACY: Peter lives with his aunt and uncle.
But notice how the dialogue in the second trailer presumably continues in the same scene:
GWEN'S LITTLE BROTHER: Did you catch that spider-guy yet?
CAPTAIN STACY: No, but we will...this guy wears a mask like an outlaw.
PETER PARKER: I think he's trying to do something that maybe the police can't.
CAPTAIN STACY: Can't?!
If what this trailer is presumably revealing, it's that Peter as Spider-Man is already a costumed vigilante before Uncle Ben gets killed. If that's the case, doesn't this essentially undermine Spider-Man's primary moral of "With great power comes greater responsibility?" After all, as every Spidey fan knows, Peter used his powers originally not to become a superhero but to become an entertainer, to use them for his own personal fame, fortune and glory, and in a moment of arrogance, allowed a criminal he could have easily stopped to escape who ended up killing his Uncle Ben. But if Peter is already using his powers to fight crime, to do what the police can't, and thus is already using his powers responsibly while his Uncle Ben is still alive, then it actually takes away one of the the most fundamental aspects of his own origin story and even his primary motivation for becoming a superhero in the first place.