Richard Parker killing the assassin that killed his wife and still successfully uploading his file before dying.
Spider-Man catching a car. It's safe to assume this movie won't be ignoring his Super Strength.
Then creating a web in mid-throw to stop another.
During the fight with Rhino, he uses a manhole cover to deflect a missile, jumps into the air swinging it around on a web-line deflecting 2 more, and uses the momentum to throw it at Rhino!
The kid that confronts Rhino at the end just before Spidey shows up. The little guy had more guts than an abattoir.
Spidey's first fight with Electro. Complete with a slowmo, 360 shot to show his spider sense.
He's dodging lightning! He's dodging FREAKING LIGHTNING! Forget about lightning-fast reflexes, Peter has reflexes even better than that!
Along with a sense that shows everyone who is in danger. The old man who's about to get clobbered with a police car, the two bystanders about to place their hands on the electrically-charged handrail, everything. And Spidey saves every single one of them.
And he does it with one webshooter. He actually instinctive goes for a two-shot solution first before realizing one is fried... and comes up with a solution with the one in those milliseconds.
Heck, ELECTRO, himself, bullets literally vaporized when they get near him, Spider-Man's webs are burned when they touch him. And he manage to take out friggin' TIME SQUARE and destroyed it, and he probably wasn't even fully aware of his abilities.
Before Spidey arrives, the NYPD's initial actions in calling for backup and clearing the immediate crowd around Electro deserves some praise in being Genre Savvy and being concerned about public safety first in Times Square. Unfortunately, after Spidey arrives, they don't handle the situation that well by firing on Electro.
Peter distracting the Oscorp security so Gwen can escape by feigning clumsiness. This may very well be the most coordinated and dexterous version of the wallcrawler yet!
The Green Goblin actually gets a few:
Before even getting his powers and after being deposed from Oscorp, Harry manages to sneak into Ravencroft, find Electro and not only helps break him out, but convinces Electro to help him with just three words: "I Need You!"
How quickly and easily that the Green Goblin deduced Spider-Man's alter-ego. Just seconds after seeing Gwen and Spider-Man both at the power station he puts together everything that Peter had said about Spider-Man, his brief talk with Spider-Man and what he knew of Gwen and Peter's relationship and realizes that Peter is Spider-Man.
The fact that he actually killed Gwen. In the few minutes he has on-screen in his villainous alter-ego, Harry delivers a bigger punch to Peter than any one of the villains Spider-Man fought in the four previous films were able to. Now that is an Arch-Enemy.
The Spidey-Green Goblin fight, for both sides and the filmmakers. The fight moves indoors, negating the height advantage of the Goblin's glider, while Gwen's safety keeps distracting Spider-man. He has the clear advantage in fighting skills, but the Goblin keeps unleashing new and surprising weapons on him. It's a constant re-leveling of the playing field, pitting both sides as disadvantages even when they both keep attacking.
Earlier in the film, Spider-Man saved a little boy from a group of bullies, then fixing his science project, THEN offering to walk the kid home. After Peter hangs up the suit for several months following Gwen's death, the same kid walks out into the crossfire of the Rhino and the NYPD, pulling on a Spider-Man mask. When Peter shows up again what does he say? "Hey, Spider-Man. Thanks for holding the fort for me." He is obviously cut from the same cloth as the kid from Iron Man 2 who distracted a Hammer Drone by showing his toy repulsor.
Spider-Man's battle with Green Goblin, it's heart-pounding and intense to say the least.
Meta example: Andrew Garfield's acting in the scene where Spider-Man finds out that Gwen Stacy is dead. If anyone still had doubts about him being able to play the Wall-Crawler, they're gone now.
Another meta example: the filmmakers. They actually killed Gwen Stacy. With the trend of fake-outs and the refusal to kill main characters running rampant nowadays in Superhero Genre, they not only killed Gwen, but kept Peter's hand in it intact. Damn.
A frequent criticism of the Spider Man films is that Spidey removes/loses his mask way to often, in increasingly contrived ways. This is the first film to avoid that. Not only does Spidey very rarely remove his mask, the few times he does, it feels a lot more justified than in previous films.
The air traffic controllers. Upon realizing the whole city's in blackout, they immediately begin writing down every planes approach, realize there's going to be a collision in 4 1/2 minutes, start a stopwatch to time it, and the second the power's back, they radio the pilots, saving both planes.
Peter remembered Max. All he knew is that he once saved this blue guy from getting hit by a car (which he'd done half a dozen times on screen at this point), and he's able to not only remember him as "The Blueprint Guy", but exactly what he said to him (You're my eyes and ears), and then Peter got his name. Considering how many people he chats with as Spider-Man, that's damn impressive.
This is a meta example, crossing with Tearjerker and Heartwarming, but Peter (as in every major incarnation) is a hero but also seems to be a magnet for tragedy. In this pair of films alone, he loses his parents to corporate corruption and assassination, his uncle to murder (aided by his negligence,) a mentor in Dr. Connors to madness and mutation (from a formula HE gave him,) an ally in Captain Stacy (not to mention his girlfriend's father,) a would-be friend and ally in Max/Electro to paranoia and more corporate scumbaggery, and his former best friend Harry to desperation and hatred. Top that off with the self-fulfilling prophecy of Gwen's death due to neither her nor Peter being able to let each other go like he promised the Captain, and neither being able to deny their own heroic natures, come what may? Yet he still takes up the webs and fights crime (with good humor and visible compassion, mind) because he knows someone has to make a difference and he has the power to do so and... you don't need me to tell you the rest. Bruce Wayne didn't lose quite as many people in the The Dark Knight Saga and arguably turned out worse. It's like Bret Hart said, "How far you go in life depends less than you think on what you pick up along the way, and more than you think on what you've got in you from the very beginning."