Just from the first two episodes alone it seems like the series will be filled with these thanks to Peter's Imagine Spots.
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.
His first three run ins with Trapster are shown in hand drawings of him being stuck on a school bus, on top of the Liberty Torch, and on the Thing's back.
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.
When the Frightful Four attack Midtown High, we get this jewel:
Wizard: If Spider-Man doesn't reveal himself, we'll tear this school down brick by brick!
Random Student: YEAH!
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!
Of course there was Spidey's first test run on the Spider Cycle, which he barely has control over, and has him driving crazy over New York.
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.
Peter shaking hands with Nick Fury-than activating his web-parachute that covers them both. "...Awkward."
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!
A lovely exchange between Coulson and Spider-Man:
Coulson: The Daily Bugle says that Spider-Man is a threat to public safety. Peter: But I'm so cuddly.
Sam proudly holding up his mashed potato sculpture of Coulson.
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.
White Tiger shreds a Doombot the minute they land in Latveria. It lives long enough to bemoan one thing before exploding:
Spiderman Describing Doom as wanted for rocking a DnD armor and green cape in the 21rst century.
"Wheel of Excuses".
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.
Spider-Man:(In reference to Thor) And you're missing the eensy weensy detail that YOU ARE A FROG!
Spider-Man to Loki: "You broke the doors! This is why we can't have nice stuff!"
Frog Thor: "Thought you could defeat Asgard's warriors? I say thee... ribbit!"
Thor talking in general while in frog form. They wisely choose to keep his deep manly voice making everything he says that much funnier.
"Fear the Frog of Thunder!"
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:
Sabretooth's completely "What the hell is going on?" reaction when he first sees Spidey in Wolverine's body trying to say he isn't, followed by the first self-shanking.
A small dog barks at Sabretooth, Sabretooth barks back, dog drags owner away.
Peter so freaked when explaining what happened to Logan he loses the Gutteral Growl and sounds much more like Spike.
"Wheel of Responses".
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.
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.
Out of Damage Damage
Spider-Man infiltrates Mac's office and destroys its security system.
Spider-Man: Maybe Mac won't notice. (Cleaning bots come in and rebuild the room) Spider-Man: OK, so Mac really won't notice.
After the first battle with the Wrecking Crew, Fury has taken every opportunity to berate Team Spidey for the damage caused, even forcing them to work with Damage Control to clean up the mess. When they finally manage to prove themselves to him, he reinstates them as SHIELD-santioned superheroes...accidentally brushing against a pile of huge, metal pipes. Said pipes start rolling out of control towards one of the damaged buildings, causing it to collapse completely. Not only do we finally get to see what Nick Fury looks likewhen he screws up, but Spidey puts the cherry on the sundae by grabbing one of the vacuum devices he and the others had been using in the cleanup effort and handing it to Fury.
Coulson: Tuck your shirt in, then you can run for your life.
Coulson: Flash, get out of here. It's going to get messy.
Thor: Beware, you are about to face the god of thunder!
Coulson: (using a jetpack, has a S.H.I.E.L.D. gun and has his tie tied around his head) And the Principal of Midtown High!
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".
Nova showing the pictures of Spider-Ham to the others (who laugh uncontrollably), showing Peter didn't quite avoid embarrasing pictures on "Picture Day."
The Iron Octopus
Spidey's reaction to seeing Norman pull a BFG on Iron Man.
Spider-man: "It's safe to say that this is a side of Harry's dad I've never seen before. Is this what he meant when he said I wouldn't understand?"
Spidey gets a dig in on Iron Man's security precautions.
Doc Ock: The arc reactor... Why isn't it recharging?! It should be self-sustaining! I built it to your specifications!
Iron Man: Off the specs you stole from me. But 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.
Not a Toy
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 colorful! (Enthusiastically rubs the shield before giving Caps a pair of adorable puppy-dog eyes)
"Big ups to my boy Spider-man! For making all of my dreams come true." 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.
"Wheel of Explanations".
The power is out, and the team changes into their costumes in total darkness. Iron Fist lights his fist up... and everybody is somehow wearing each other's costumes! Including Spider-man dressed like White Tiger!
Spider-man: Let's all agree? We never speak of this again.
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.
Kraven the Hunter
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!
When Spidey and Power Man discover that Luke's parents are working for Scorpio:
Spider-Man: This is gonna make an awkward "Bring-your-son-to-work day"!
Blade and the Howling Commandos
Coulson gives the info dump about the ankh. No one comments, but to do it, he uses a hologram program that turns the SHIELD helicarrier into an Egyptian temple and he's the only person to get a costume switch. He now looks like Indiana Jones. To top it all off, he knew exactly where they needed to look because he was a gold card member of the Museum of Natural History's FANCLUB.
"Yeah, it's code for 'Dracula's coming back'"
Spidey's exchange with Blade:
Spider-Man: I see what you're doing. You sent Power Man to punch a hole because you knew his invulnerability would protect him, right?
Spidey's reaction to Max the Invisible Man...right after he gets pantsed by him and he actually gets excited at the idea of meeting Max.
Spidey once again finding himself low in the hero hierarchy ranks.
Spider-Man:15!? Behind Hawkeye and Nova? And who the heck is Squirrel Girl?
Loki pointing out that Spiderman is hurting his own body which will hurt like heck. When Spiderman try to correct this by electrifying Loki's body, the Asgardian just scoffs as that wouldn't count as a stubbed toe for his kind.
In The Savage Spider-Man, we have the Man-Spider. Just... Man-Spider. Not only does he still break the Fourth Wall (though all he can really do is growl and snarl), but he also tries to eat a t-rex after beating it by roasting it over an open fire by the tail. And let's not forget the fact that, since he's more spider than man, he fires webs from where spiders normally spin them.