While the parent side-story was an interesting new angle, I'm referring to all the other familiar fat on the bone that took too long to develop:Minor spoilers (Click to show)
Establishing Parker as a science nerd, him being bullied at school before eventually humiliating the bully with his newfound powers, the clumsy attempts to get attention from the pretty girl, the science lab experiment gone wrong to give him his powers, the argument with the uncle, the random theft by a thug which Parker ignores that leads to his uncle's death, the early failed attempts to control his new powers, the evolution of getting his costume...
...because most of us know the general outcome of these plot points going into the movie, there is absolutely zero suspense. It took a long time to get past Spiderman 101 before the movie got going.
Batman Begins handled the retelling of Wayne's origins a lot better IMHO. They quickly explained his relationship with his dad and how he was killed. However hallf of that initial act was about training and fighting with ninjas in the snowy mountains. Simply put, the first act of The Amazing Spiderman needed more ninjas. Or vikings, or amazons or something.