We might as well do this in bullet-format:
- An actor that actually seems like a real-life Peter Parker to me. Tobey Maguire has a slow, sort of stumbling persona on screen, and Spidey is the personification of quick-wittedness. It was a poor casting IMHO.
- Mechanical web-shooters. Check this video for Andrew Garfield's confirmation of this aspect. I won't get into the utter wrongness of Spider-Man's shooters being portrayed as organic. It's like turning the Punisher into Bushwacker.
- Emma Stone is way hot.