The Cut during Fury's lecture about how other heroes "started out clueless", to Iron Man first trying out the MK. III Armor, ricocheting around his private garage before crashing into and destroying one of his cars, embedding himself in it upside-down, and remaining stuck there for a couple seconds while the alarm blares for comedic effect.
Of course there was Spideys first test run on the Spider Cycle, which he barely has control over, and has him driving crazy over New York.
Blink and you'll miss it, but in the opening sequence in "Great Power", Spidey does a triple axel as he sails across the Jumbotron screen.
In "Great Power," during a fight with the Frightful Four in Midtown High, Flash Thompson tells Spider-Man that he's his biggest fan and he wants to help. Remembering how he gets stuffed into a locker by this jerk on a daily basis, Peter responds as thus:
Spider-Man: Definitely, "bro." (Opens one of the lockers) Step in.
Flash Thompson (eagerly stepping into the locker): Now what?
Spider-Man: Wait for my signal. Jump out, and we'll surround them. Remember, wait for my signal. (Slams the door shut) Immature, I know, but it felt so good!
White Tiger poking fun at Nova in "Great Responsibility." It's the insultingly cutesy-wootzy tone to her voice she adds that does it.
White Tiger: Look who thinks he's still in charge. It's so cute.
Followed immediately by:
Spider-Man (chucking aside a torn up robot arm): Next?
Fury: Web-Parachute test. (Smirks) See you tomorrow.
(Cue the floor opening up and sending Spidey plummeting to the ground below, screaming at the top of his lungs like a little girl all the way.)
In "Great Responsiblity," MJ is wondering who Spider-Man could be, saying he could be anyone, a teacher, a student, and then, just like clockwork, Stan the Janitor walks by.
Stan (jokingly) Thwip! Thwip!
Minutes after that, Spidey meets Dr. Curt Conners, who actually manages to put one over on him by feigning his canonical missing arm.
While test-driving the Spider-Cycle for the first time, Spidey lands on the Jumbotron of J. Jonah Jameson in the middle of his daily rant against superhumans. He promptly uses the bike to draw a mustache on him via skidmark.
Near the end of "Great Responsibility" when Peter finds out his teammates are now going to his school he says he has to talk to a guy. Cut to him at the Principal's office demanding a transfer. Funniest part? The Chair Reveal that Agent Coulson is the Acting Principal and Fury wants him to stay right where he is.
Coulson: Acting Principal Coulson. *Spidey hands* Thwip thwip!
In "Doomed", after Spidey captures "Doctor Doom", he Imagine Spots a scene where he presents "Doom" to Fury at a dinner table. The funny part? During the scene, the tied up "Doom" demands to have a banana split.
Another moment from "Doomed": Sam proudly holding up his mashed potato sculpture of Coulson.
Also "Doomed": Agent Coulson losing his mind, as acting principal.
Fury: He's gone native!
Coulson prattles on about the school's budget again, causing Fury to rubs his temples.
Fury: Coulson, we need to talk priorities.
And during the fight against Doom, when Spidey and Nova both go after Doom at the same time:
White Tiger: Stupidest. Boys. Ever. (explosion) Iron Fist: As a boy, I second that.
Power Man's foot being burned by a tiny, squeaky Doombot.
Spidey and Nova's imaginary faces after White Tiger calls them Dork 1 and Dork 2.
As the team has to clean up after Spider-Man and Nova's mess, Iron Fist provides an... interesting, zen rebuttal to White Tiger's complaining.
Iron Fist: The mightiest tornado gives off the gentlest breeze only when temperatures cool down.
White Tiger stares blankly at Iron Fist
Luke Cage: He does that.
In episode four, "Venom":
After Venom crashes a party at Harry's house, everyone hears the crashes. Nova's reaction?
Sam: I hope he rented a lion! (beat) What? Rich people rent lions.
As guests are running for their lives, one girl stops, screams, gives Harry her number, and screams again before finally running off.
Also, when MJ saves Harry from falling to his death by grabbing the front of his shirt:
Harry: GAH! I think you just pulled out my only chest-hair.
Afer the battle, Luke and Ava pull Danny free from the Venom-goop that had stuck him to a wall. Unfortunately, doing so ripped off his costume in the process (save his mask), revealing that he wears briefs the same color as his uniform, with a tiny dragon symbol in the front right corner.
Iron-Fist/Danny (smirking nonchalantly): (shrug) It's a monk thing.
MJ instructing Harry how to use a mop while they clean up the aftermath of the party/fight.
Again in "Field Trip," Spider-Man's Imagine Spot during the master dwarf's lecture as he hands out weapons to the others, but tells Spidey he doesn't need one because he's had his power inside him all along, but that he has to accept his role as leader to fully unlock it here:
In "Me Time", when Peter finds a SHIELD hidden camera in his house, he looks up to the heavens and screams “FUUUUUURRRYYYYYYY!!!!!!"
Lets not forget that after Fury saves Peter at the end of the episode, Peter asks Fury to delete the security footage that SHIELD places in his home and Fury agrees and will delete in 24 hours. 23 hours and 23 minutes later, Fury shows the other trainees Parker's embarrassing moments before deleting it.
Peter's nightmare, including Aunt May with a spider head and bright hat.
One of his extra arms tries to pick his nose as he's talking.
Doctor Strange: Honestly, Danny? This was the best you could do?
Iron Fist: A dull blade can make an excellent hammer.
Spider-Man: I heard excellent and dull. Am I offended or not?
Doctor Strange gets a nice one over Spidey and Iron Fist: "Speaking of nightmares, ever had the one where you had to get back to school before anyone knew you were missing?" Cue Spidey and Iron Fist with panicked expressions on their faces.
When Spider-Man is looking for something to pass off as a science project in order to meet a deadline, he remembers that Curt Connors gave him free access to his laboratory and equipment. Spidey's good and bad angels clarify:
What Dr. Connors Actually Said: I want you to know, Spidey, I have an open-door policy. If you need any help for yourself or your teammates, I'm here.
Mary Jane telling off Galactus for trying to eat the Earth. Spidey admits it didn't happen, but it's funny anyway.
Spidey thinks his teammates ditched him for lunch after not getting a response.
Wolverine at Anger Management...with Sabertooth in it and Spiderman caught on the crossfire.
As the gang confront Beetle, Nova says that 5 against 1 may is not a fair fight but these guys wants some payback. That is until Beetle takes out multiple missiles from his suit causing the group to rethink their numbers.
As the gang relax at a beach, Ava is seen studying, but Peter busts her when he yanks the book away and finds that it's a romance novel. She grabs it back from him and enthusiastically returns to reading it. What makes the scene funnier is that the book is titled "Thundering Hearts" and the cover model looks suspiciously like Thor.
This isn't the first time we see her read romance novels, she's pictured holding a book titled "Fang Love" in one of Spidey's Imagine Spots to what he expects her to be doing, suggesting Spider-Man is well aware of this and a bit of Foreshadowing to this event.
Luke Cage and Spider-Man discover Sandman's story, but they get sidetracked by the depictions of Nick Fury and Agent Coulson. While Sandman is chasing after Nova.
Luke Cage: Sweet Christmas! Tell me that's not Nick Fury!
Spidey: Super-fly eye patch and all. Coulson rocking a ponytail?
Luke: Copy me?
Spidey: (snaps a picture with his cell phone) Totally copied. To everyone.
Spidey lamenting the fact that he gets no respect.
Spider-Man: I save the world too. But do I get a billboard? No, I get...
Doc Ock: The arc reactor... Why isn't it recharging?! It should be self-sustaining! I built it to your specifications!
Iron Man: My specs. I never keep everything on a computer. All the good stuff stays right up here. (points to head)
Spider-Man: Except for the activation codes, apparently.
(dramatic music stops)
Spider-Man: Shutting up now.
The team is getting schooled by Captain America by every definition of the word. Spidey tries to web Cap, and gets Coulson instead. He ends up ripping off Colson's jacket and shirt... to reveal that he's wearing a replica of Cap's uniform under them.
Spider-Man imagining if he had Cap's shield.
Spider-Man: Avengers assemble! (Iron Man, Thor, and Hulk come in) Avengers disassemble! (they leave) Avengers assemble again! (and they come back)
When the shield lands on Dr Dooms embassy, Spider-Mans ask for the shield back, Doom replies with a missile.
Spider-man imagining that with Cap's help, Doom would just give them back the shield.
Doom: (sniffs) I'm sorry. Here, take it... I just wanted to play with it for a bit.
Spider-man: Oh, I know, right? It's so light!
Doom: And shiny! (Enthusiastically rubs the shield before giving Caps a pair of adorable puppy-dog eyes)
"And let's all give a big ups to my boy Spider-man!" Those words should never come out of Doom's mouth.
Spider-Man just discovered that it was Norman Osborn who was after him, he didn't now this and looked back at some cuts, where he is to busy hanging out with Harry, and was oblivious to Norman who was destroying pictures of Spidey who's right in front of him.
Peter: (To Harry) Oh yeah? Well your dad's a monster!
Norman: (comes up behind him, speaking in his normal voice and dressed in a suit despite being the Green Goblin) I'll be back later Harry. I left a thousand dollars in case you get hungry.
During the Hunt, Spider-Ham hides in a trash bin. Que Loki, disguised as a mime, indicating the Hunters where Spider-Ham is. The Hunters, not understanding what Mime!Loki is doing, stand there. Finally having enought, Loki just flat out tells them where Spider-Ham is.
Spider-Ham: "You put all mimes to shame".
When Rhino is out to get Flash, Spider-Man tells Flash to run by getting in the school bus. Flash says he doesn't take the bus, but when he sees Rhino, he chickens out to the bus.
At the end of "Kraven the Hunter", Spider-Man and White Tiger have a heartwarming moment together...which is then interrupted with Nova with his phone camera out and aiming a beam of light at her.
Nova: Hey, is she still catty? Get the dot, kitty! Make the internet smile!
[White Tiger promptly attacks him, causing him to drop his phone]
Spider-Man: [picks up the phone] Go get him tiger! But wait for me! Cat videos are huge!