Although I don't agree with Mr. Parker's assesment of the films, I do agree about not liking the organic web shooters.
And here's why:
In the comics, many times during a vital part of a fight Peter would run out of webbing. Or he would know that he didn't have enough fluid left to say pursue a lead or go somewhere he needed to go before refilling. This created many instances of dynamic tension. Suddenly, here is an outside force stopping Peter from fullfilling his obligations. And that is what Spiderman was all about. Man's battle with the forces of nature and environment. Look at most of Spidey's villains. Many either elemental in nature or based upon things found within nature. i.e. The Vulture(animal), Rhino(animal), Kraven(animalistic), Sandman(elemental), Electro(elemantal), the Lizard(animal), etc. etc. Even The Green Goblin was a man who had enhanced his nature, which if anyone remebers is what the Goblin Formula was created to do. Not JUST give superhuman strength.
Now, this is old school Spidey I am talking about of course. None of this Venom or Carnage bullsh*t.
And this same thing that made me dislike the first movie, brought me back around in S2. Suddenly he couldn't rely upon his powers completely anymore. Suddenly he was running out of web fluid. So they brought that struggle back into play.
'Nuff said.