The only part I think Peter is being inmature is (SPOILERS ABOUT GWEN) [BLACKOUT]when he follows Gwen around NY after they break up, pretty stalker like[/BLACKOUT]. The relationship with Gwen comes and goes in the movie, but Andrew and Emma are great. No other couple could be better in screen.
In general, I think the movie portrays the character of Peter pretty well. He's Spider-Man, but he also has this other Peter Parker stuff floating around that kills him, like his parents or his relationship with Gwen and Harry. It's not exactly like Spider-Man 2 though, it flows better.
Worst part by far is Dr. Kafka. I don't know who the **** thought that character would be a good idea, thank good he only shows up like 3 min total.
Electro could be developed better during the final battle (motivations pretty much... ehh), I liked Electro the rest of the movie and I think it has a the Max Dillon character is well developed (it's goofy at the beginning, but it improves).
Spidey is awesome, not only movement-wise, but personality too. No movie has captured Spidey better than this.
Harry Osborn, well, mainly because of Dehaan, is a good character. Much better than in the Raimi trilogy. It picks up trails of the Norman Osborn for the comics, but with much different motivations. As Green Goblin, I have no problem with it, he's like 10 min in screen time, but damn, what a 10 min. This is not like Venom that had a lackluster fight. Dehaan is a much better Goblin than Dafoe or Franco was in two films with a much limited screentime.
Rhino is in there. That's all I can say, pretty much. The looks are cool, the tie-in with the [BLACKOUT]Sinister 6[/BLACKOUT] is interesting. It works as a proof that Spidey has a universe of supervillains around him and that he doesn't need "the villain of the week" for a fight.
Aunt May is a little underdeveloped, she has a storyline that is tied up pretty fast in one particular scene, and apart from some scenes at the end [BLACKOUT]during NY's blackout[/BLACKOUT] she's not that much in it. She's a big important part at the epilogue of the film though.
Also (MAJOR SPOILERS) [BLACKOUT]Gwen's death couldn't be done better in film. I'm pretty sure it's impossible to surpass this scene. The whole theater was silent, a lot of the theater had a tear when blood comes out her nose, and specially when Peter hears Gwen's speech along with the flashbacks. The silent scene of Peter visiting the grave during the seasons is brutal[/BLACKOUT].
I loved the film, it's not perfect, but it's the best Spider-Man film by far for me. But it's okay, I get that it might not be what everyone was expecting it.