I watched it in good ol' fashioned 2D.
He's definitely not clumsy, but he's still a "nerd" -- member of the debating team, social outcast (he doesn't even socialise with other nerds), is still a whiz kid (check out that remote computer controlled lock on his bedroom door!) etc. They've still maintained the fundamental part about Peter being a highly intelligent but socially awkward/isolated school kid. Still the outsider.
Hmmm... I guess. But if it's like real spider webbing then it's pretty hard to see (how often have you walked into a spider's web in low light!) and it may even decay after several hours or a day. Also -- he shoots the webs up pretty high. The police would need to expend considerable resources to get up to those places to collect samples, and further resources to have them scanned in a lab. These are kind of resources that police often will spend when there's been say, a homicide... but since Spider-Man isn't actually wanted for murder (the arrest warrant stipulates that he's wanted for questioning) then perhaps they're not willing to do it. But I think the webbing's best defence is the fact that it's hard to see... kinda like the perception filter on the TARDIS.
This actually makes me think of something else that seems odd in this movie -- the two cops who shot at Spider-Man. Cops shouldn't (wouldn't?) do that. In both instances Spider-Man was not presenting a threat to those cops. The first time he actually had his hands up and was just talking to the cop before he opened fire repeatedly! The cop who shot him did so when Spider-Man was fleeing (especially after Captain Stacy had let him go and told officers not to fire). Cops get in trouble if they so much as draw their firearm without just cause... heck, even when cops do fire at someone who's attacking, they sometimes get in trouble! But to open fire on a suspect who's not attacking anyone at the time??
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P.S.: RE: Web shooters
One change of the franchise to reinvent the hero for the film was to go back to the original source material in the mainstream comics of Spider-Man having artificial web-shooters. Writer Geoff Boucher of the Los Angeles Times was skeptical of the change feeling that it's too hard to believe that a financially strapped young man to conceive a wrist-worn device that can instantly produce a strand of synthetic webbing. Even though there was skepticism of the change Webb himself felt that "the web-shooters were able to dramatize Peter's intellect". Webb paid attention to the question of "How would a kid make it?" And then took some license with it.
http://en.wikipedia.org/wiki/The_Ama...282012_film%29
http://herocomplex.latimes.com/2011/...#comment-76324
http://herocomplex.latimes.com/2011/...t-but-do-they/