What worked:
Gwen Stacy
The best thing in this movie would definitely be the relationship between Peter Parker and Gwen Stacy. Garfield and Stone had great on-screen chemistry, and it made for a believable (although somewhat illogical and forced) romance. I would be lying if I didn't get teary eyed for them by the end.
This is also thanks to the charm and character that Emma Stone brings to the movie. Also, if we're keeping score, Emma Stone's Gwen Stacy >> Bryce Dallas Howard's Gwen Stacy > random extra walking in the background > Kirsten Dunst's Mary Jane Watson. I think it's time we found a Black Cat, don't you?
Web swinging scenes
A lot of the time, I kept noticing many iconic Spider-Man poses. Every time Spidey goes to swing around, you can count on specific video screencaps looking like comic book covers, which I thought was a great nod.
The first person shots were also quite astounding. They did a great job of putting the audience in the red and blue tights. I'm quite sad there wasn't more, and I bet that would've looked bad ass in 3D. In the same vein, the parkour/ freerunning looked really good and lent Spidey a lot of authenticity especially since most of the other scenes were all "fuck you, laws of physics."
Sciencey Parker
Spider-Man has always been a science nerd and that's always been one of his greatest assets. I actually dislike that it was quite underutilized in Raimi's movies. Those web-shooters weren't there just for fan service; it served the plot and explored Peter's character's further. And they were just plain cool to look at.
Snark
Although Raimi's Spidey didn't have sloppy writing, I find Webb's script a little more engaging and a heck of a lot funnier at times. Garfield's Spider-Man's quips were just generally more Spider-Man-like and had that much more wit to them. Maybe it was in the delivery also.
Garfield
I've been reading a lot of the same sentiment on Facebook and Twitter - Andrew Garfield is the new "Christopher Reeve" of the Spider-Man character. I prefer the term "new Robert Downey, Jr." Even though Parker's character in Amazing Spider-Man wasn't exactly what I was hoping for, I think Garfield does a much better job at being Peter Parker than Tobey Maguire. Sorry, Tobey.
The costume
As much as I hated it in the promotional art, I have to admit that the new suit worked well for the film. In action, especially under much of the dark lighting prevalent in the movie, the differences were subtle enough to not be so jarring for long time Spidey fans. Also, those sneaks are pretty damn cool.
Flash Thompson
He's more than just a meathead bully. 50 years of character development made sure of that and this film just nailed it.
What didn't:
Peter Parker didn't feel like Peter Parker
But then again, this is a result of having an expected character already in mind, which is both the strength and yard stick of all film renditions of established franchises. If you didn't know who Peter Parker was, this characterization makes sense and it made the audience feel something for him, even if it was annoyance. The comic book fan in me was going "Since when was Peter Parker a douchebag to Aunt May and Uncle Ben?" If you manage to separate those two universes, though, then you'll enjoy the film even more.
I don't think this is because of Garfield's performance. Instead, this is more of a result of Webb's direction more than anything else. Again, it's not bad; just not the way comic book purists would expect.
Worst kept secret
If there's anything Spider-Man protected more passionately than anything, it would be his secret identity. It just rubs me the wrong way every time his mask gets taken off, and how every important person in the story knew exactly who he was. Hell, even some thugs knew what he looks like.
Too much grit!
Just when you thought gritty reboots of beloved franchises were dead, along comes The Amazing Spider-Man. At times, the grounded angst felt like it was suffocating the very essence of the character. What is this, the fucking 90's? The dude wears blue and red; that level of gloom doesn't really work and it often times clashes with the idea of how Spidey should be. It worked for Nolan's Batman because Batman is Batman. Let Spider-Man be Spider-Man.
Raimi VS Webb
Even though you know you shouldn't compare the two, it's very hard to resist. The similarities were just too obvious. In fact, a lot of the elements of Webb's take mirrored Raimi's, and this isn't due to the source material. Rhys Ifans' Lizard's psychosis and paranoia are very similar to Willem Dafoe's Green Goblin's, even down to the disembodied creepy voices in their heads. It's practically the same character, just given different motives and power sets. It doesn't help that the two antagonists both eventually learn of Spider-Man's true identity giving them the same relationship with our hero.
I wouldn't say that The Amazing Spider-Man is now the ultimate Spider-Man movie. Sorry, that still belongs to Raimi's Spider-Man. It comes hella close, though.
TL;DR
Spider-Man > Amazing Spider-Man > watching paint dry > Spider-Man 2 > watching a wall be a wall > Spider-Man 3
If you're a Spidey fan or if you're into action packed chick flicks, give this a once over. And when the Blu-Ray comes out, buy it.