Peter again lying to Aunt May, who's trying to hide her trainee nurse uniform by pretending to be upset that the last time he washed he made everything blue and red. This ends with Peter calling her "laundry sheriff."
The tone just implies that Peter thinks she's getting absurdly controlling. After all, he was just washing his American flag.
Spidey's first meeting with Aleksei Sytsevich:
Spider-Man: You can call me Webhead, you can call me amazing, just don't call me late for dinner, y'know what I'm sayin'?
Peter sending his latest batch of Spider-Man photos to the Bugle, suggesting that Mr. Jameson consider that Spider-Man's a hero. He swiftly receives an email back from J. Jonah himself, simply titled "WRONG!!!"
The scene where Peter delays the security guards from reaching Gwen, acting like a complete klutz, before leaving after he knows they didn't catch Gwen, topped off with the end of the sequence.
Peter: I'm all thumbs today! As he walks down the hallway, Peter hops in the air and kicks his heels.
Not only that, but while he was klutzing, he tied together one person's shoes, stole another's taser, and flipped a cart on top of the third.
Harry and Peter reuniting - Harry jokes that Peter's braces being removed just means that there's nothing to distract from his unibrow, and Peter teases Harry over the large number of staff who dress him and style his hair. Harry counters that whilst one of his man-servants handles the blow-dryer, Harry works the comb himself, so he's not completely incompetent.
Harry's comment about dating supermodels just being exhausting, and Peter's sarcastic "I know."
Peter's phone goes off, waking him up. We see a web fly into the screen, and quickly pull a crowbar out of the screen - this is then followed by a clunk and Peter groaning, and a second web pulling Peter's phone out of the screen. Cut to Peter, having apparently slept on the ceiling, rubbing his face as he answers the phone.
The science montage before this scene in general. Peter is trying to make his webs electricity proof, but fails spectacularly. He even accidentally makes one of his webs burst into flames.
Made funnier by his ever more elaborate improvised safety equipment and using the fire extinguisher on the car battery.
Near the beginning, there is a montage of Peter repeatedly coming home to take off his suit after a day of crime-fighting. The suit is usually covered in some form of muck, grime or something ridiculous - at one point there is feathers.
Then there's the time where Peter inexplicably has an entire dead fish.
And then there's him picking up some cold and flu meds for a bad cold, only for the store to be held up by an armed gunmen, who Peter has to deal with after a quick off-screen change, before trying to buy his medication, while still in the costume. Bonus points for his awkward sneeze inside his mask.
The store clerk calls him "the Spider-Guy." When Spidey corrects him, he's so stuffed up it sounds like he's saying "Spider-Bad."
Spider-Man in a fireman's helmet. That is all.
Max's whole pretend conversation with himself as he imagines Spider-Man caring enough to celebrate his birthday.
Spider-Man whistling the 60s Spider-Man theme song during his first fight with Alexsei. While tying him up with webs then pulling down his pants.
The scene where Harry and Electro torture Menken, complete with Harry calling Menken his "Fairy Godmother", whistling the tune of Final Jeopardy! (possibly unintentional Product Placement), Electro interrupting Menken by shocking him to near death, and then restarting his heart with another electric shock, complete with Harry saying "clear", was funny in a very twisted way.
It also works if you consider Harry may have been calling Electro his Fairy Godmother (Blue Fairy ala Pinocchio).
Spider-Man desperately using his webs to try to catch the plutonium test tubes during the car chase.
The scene where Gwen is on her way for her oral examination to get into Oxford, only to be delayed further by Peter's awkward speech about the UK. It's even funnier when you remember that Andrew Garfield grew up in the UK and is a dual UK/US citizen.
Spider-Man and Electro are fighting it out in a power plant. Electro phases between these magnetic rods that make a tone every time he does, making a rhythm. After getting knocked around, Peter laments that he "hates this song". The song in question? "Itsy-Bitsy Spider."
After the above scene, Electo has Spidey at his mercy and preparing to finishes him off...
The whole chase sequence at the beginning, from Spider-Man dealing with the robbers, as mentioned catching all the radioactive canisters while bouncing around the truck, then having to go after one that managed to escape his grasp. He manages to retrieve it, only to be hit by an incoming police truck (complete with Girly Scream) and stuck to the fender.
Even better, Gwen calls at that exact moment to warn him their graduation is starting.
Peter: Hey I'm..I'm sorry I'm running a bit late and I got stuck in some traffic.
Gwen: Your timing is terrible. It started already.
Peter: Yeah, I know, I'm sorry.
Gwen: Where are you?
Peter: (As the truck passes by the streets) 1st and Broadway. 2nd and Broadway. 3rd and Broadway. Five minutes, Ten tops.
Gwen: (Hears sirens in the background)...Are those sirens?
After turning up at the 2011 San Diego Comic Con in a cheap Spider-Man costume and gushing about his love for the character, Andrew Garfield was unfortunately running late to the 2013 panel for the sequel. Thankfully, Spider-Man himself managed to make it instead, and promptly geeked out upon meeting Jamie Foxx, but sadly had to leave before Mr Garfield could arrive to meet him. Strange, isn't it?