Per the Wiki site on Spider-Man's webcasters,
In the original comic book Peter Parker develops the webcasters on his own as "an extremely intelligent and creative" scientist. Per the same site this is further explained in 1994's Spider-Man: The Animated Series. In it Parker explains that when he became Spider-Man, he also became subconsciously aware that a combination of certain enzymes would create a strong, sticky fluid reminiscent of a spider's webbing. He then built web-shooters as in the comics.
However, in the Amazing Spider-Man while we see Andrew Garfield as Peter Parker assembling his web-shooters, the Oscorp Biocable box on the table (and accompanying voiceover description) insinuates his source of webbing is from Oscorp. It never shows any other location/place/source that Peter might make his own webbing. If that is the case, why wouldn't anyone think to try and trace purchases of the webbing to identify Spider-Man? Also, even if Peter did happen to start making his own webbing, wouldn't investigators initially assume it MIGHT be Oscorp bio-cable and attempt to trace at least his first purchase?
If perhaps Peter didn't purchase the first box, wouldn't the police still make an effort to trace who might have had access to obtain biocable? E.g. if Peter obtained it through his internship contacts while at Oscorp, he would likely show up on a leads list of suspects. A routine background check asking about him at school would quickly turn up the fact that he had behaving oddly and demonstrating superior physical skills.
In fact, Dennis Leary as Captain George Stacy alludes to the fact that Spider-Man "makes mistakes". He is sloppy and leaves clues. I would think leaving the biocable webbing around at his activity sites would be a pretty good lead on which to follow-up.
Is there something in the movie I might have missed on this that someone can help point out to me?