The little Flash Back to when Peter and MJ were best friends as kids. Talking about how they "ran away forever (being unable to cross the street, they just walked up and down the driveway)" and how they decided to finally "get serious" when they were 12, kissing and immediately going "eewww!" at the same time seconds after. It's really sweet to see that, and to see how they're still best friends to this day.
And again, when Peter flashes back to how he first met and became friends with Harry Osborn. Harry and Norman picked Peter up when his bike broke down in the rain, giving him a ride back home. Norman hoped Pete would be a good academic influence on Harry, something he wasn't too keen on. Then Pete started to talk about his Uncle and how he really took care of him and wanted what was best for him. This made Norman genuinely smile, something Harry had always wanted to see.
Harry: He's smiling. My dad is actually smiling! (Turns to Peter) How'd you do that? Peter: It's a gift. Peter:(narrating) And since that day, we've been best friends forever.
And it really is sweet that Harry loves his father so much that him just smiling makes Harry's day.
Fury gets majorly angry that one of them dragged the team into a fight with Doctor Doom and nearly destroyed both the Helicarrier and New York. He says that the one responsible should step forward, because they're off the team. Spider-Man goes to take the rap, and just as he does, the rest of the team does with him. Sure, they may fight, they may get on each others nerves, they may drive each other crazy, but when it comes down to it, they're a real team. They stick together, and they stick up for each other. Fury's response?
Fury: Don't ever let it happen again... (smiles) Team.
Even after Harry's hurt by how Peter's been spending more time with his "new friends", when the Symbiote's on the loose in his apartment, he repeatedly asks about Peter and whether or not he got away safely. Likewise, it's seeing Harry that gives Spidey the willpower needed to break free of the Symbiote.
And before that, Peter's mental exposition on why Harry is the best Best Friend ever, even saying he wouldn't have lasted this long in high school without him.
The Hulk: "Humans! Stupid Except for Bug Man! Bug Man good smasher!"
Wolverine, too, when he tells Spider-Man that he's got it good and gives him a smile and a thumbs-up before leaving the SHIELD Helicarrier.
Peter's flashbacks to Uncle Ben in "Strange". Also, Peter telling Danny that he's worthy to be Iron Fist, and showing how much respect he has for his teammate.
Danny sincerely thanking Peter for believing in him.
The episode "Strange" has the villain bring Uncle Ben back in the dream world to haunt Spider-Man about how he couldn't save him. Instead, they just greet each other, and Uncle Ben tells Peter how proud he is of what he's doing, and gives him encouragement. All Peter has to say is:
Good bye Uncle Ben. I miss you.
The fact that that is their only exchange shows that Uncle Ben died with absolutely no regrets.
Luke admitting that it wasn't all Peter's fault that the adventure that day happened, they were supposed to be partners even though Peter said he could handle it, Luke shouldn't have expected him to do it all alone. He also tells Peter, when he's dragging him into the helicarrier that he wouldn't let him take the rap alone either.
There's also a small bit with Harry and Danny being lab partners and actually being happy and bonding over it. Especially since a few episodes Harry didn't want anything to do with Peter's new friends until the end where he agreed to try. Which he did.
They even do air guitar riffs together!
Home Sick Hulk
Spidey and Hulk's interactions.
Peter spends most of his time lying to Fury in order to cover for Hulk, aww.
I Am Spider-Man
Flash Thompson of all people gets a moment or two. After episode upon episode of being an all around jerk, as well as abandoning Harry to Trapmaster and trying to use Peter as a shield against Venom. Flash (while wearing the spider costume) sees Peter trapped under a statue, then he actually runs back and tries to help him.
The Iron Octopus
At the end of episode, Iron Man gives some helpful advice to Spider-Man, advising him to use his instincts. Then it becomes a funny moment when Tony suggests himself as a potential role model and if they hug, he's blasting Spidey to Detroit.
Captain America addressing Coulson by his first name. Coulson is just so flabbergasted it's adorable.
The Attack of the Beetle
Peter Parker has complete trust in Coulson to keep his two lives separate. It's really nice how he's more worried about how weird it is that his aunt is going out with his principal then if Coulson will divulge the fact he's Spider-Man or Coulson is undercover.
The Rise of the Goblin
Peter calling Norman out for his poor parenting of Harry. Doubles as an MOA, as Norman is currently the Green Goblin, and Spidey is more than holding his own while giving his "The Reason You Suck" Speech.
After the Helicarrier burns down, Luke mentions their home is gone. Peter immediately offers them his place. To top it off, Sam brings flowers and offers to do the dishes (which comes across as a little strange, coming from him).
And Aunt May agreeing to go along with it immediately.
When describing Luke, Peter says "Big biceps, bigger heart." In fact, he's quite flattering towards all of them, but that one the most.
It was good to see all the speechs get through Flash's thick skull and give him some character growth.
Flash trying to apologize, and later defend Alex was nice to see.
The episode ends with some of the nicest compliments Spidey has ever gotten on the show.
Kraven the Hunter
Ava and Peter bonding in "Kraven the Hunter", with noteworthy moments being Spider-Man talking Ava out of killing Kraven and when she later hugs him.
The Sinister Six
"Spider-Man... is... my... friend!" Also counts as an MOA.
Spider-Man is advised by Nick Fury that a true leader never gives up, and thus resolves to never give up trying to help Doctor Connors.
The end where Peter and Harry go to the movies after reconciling. Especially since the reason they reconciled was Peter pulling a successful "I Know You're in There Somewhere" Fight on Harry, reminding him that the real Harry would never give up on his dad.
Bonus points for the end when Harry gives Peter a lift. It was raining, just like when they first met.Especially since the scene in the car implies that Harry knows, or at least is starting to catch on, that Spider-Man and Peter are one and the same. Even though he's not ready to forgive Spider-Man, he's at least ready to try with Peter.
Green Goblin telling Harry that his "father would be proud of him" would be this...if it weren't for the fact that he drops Harry from a great height immediately afterword. Plus that crazy Slasher Smile laugh...
The bit at the end of House Arrest.
The episode "The Man-Wolf" had some nice bonding moments between Spidey and John.
Fury stepping up to defend Spider-Man from Jameson.
The biggest surprise of the episode is the fact that Nova saves Spider-Man's life, and doesn't rub it in Spidey's face! Is Nova actually getting nicer?
Journey of the Iron Fist
Danny goes back to Kun Lun, leaving all his worldly possessions with Peter. Peter realizes that this also means the huge Mega Corp. Danny inherited, which would make him rich beyond belief. After the Imagine Spot is over, however...
Spider-Man: Rich would rock, but I'd lose Danny. It wouldn't be enough, obviously. *jumps on a plane to follow him*
When it looks like Danny will be staying in Kun Lun permanently, he gives Spider-Man a massive Man Hug.
The Incredible Spider-Hulk
Spider-Man's and Hulk's friendship.
Stan By Me
The ending not only reveals that Stan the janitor knows Peter's secret identity. Stan also reveals that he's one of the oldest shield agents around, and was one of the guys who came up with the organizations name. One of the most heartwarming nods in the series so far.
Deadpool's reunion with the team. They seem to be the only people in the show who genuinely like him, and despite his beliefs that S.H.I.E.L.D. is "brainwashing" them, he encourages them to stick with Fury's training.
It's revealed that while Harry and Spider-man still aren't on good terms, Peter still gives him news about his dad as Spider-man, and Harry is willing to hear it without attacking him. At the end of the episode, Peter gives him the news on his dad being supposedly (this is Doc Ock's work, so we'll have to wait and see) cured, and shows him a video of his father resting.
When Luke discovers his parents working for Scorpio.
Spider-Man: Wait, your parents? You mean your mom and dad?
Power Man: You know another kind?
Spider-Man: Yes, I do!(an image of aunt May appears)
Luke and Peter interaction at the end of the episode.
Spider-Man going to help Luke save his parents.
Even Fury gets his this episode; he goes straight into manly-hug mode on seeing his old friends alive and well.
The ending, where Spidey gets his due from Cap and even Wolverine for stopping Arcade.
Second Chance Hero
There's a lot of ambiguity on whether or not Norman Osborn has really done a Heel-Face Turn and thus everything that happens involving him could become Harsher in Hindsight, but one thing's for sure: Peter and Harry have reconciled.
The Return of Andy/Awesome Android and how Spidey reacts to the big guy. Even after Awesome and how he caused a lot of destruction he caused, it shows that Spidey still has a soft side for the big guy.
Spider-Man wanting to help Sandman have a Heel-Face Turn and Sandman thanking him for giving him a chance. Even though it it failed miserably, it shows how much of a good guy Spidey is.
Spider-Man separating his team in cells and as he fought them one by one as he reminded each of them of events each of them had as a team.
The team actually being happy with Spiderman being a Avenger. Even though Nova and White Tiger act aloof afterwards Power Man translates it as them missing Peter. Heck, when Spiderman return to SHIELD his team look as if there ready to tackle hug him, happy at his return.
Cloak and Dagger's interaction. They may have trust problems with other people but not with each other.
The password for Norman Osborn's computer is 'Harry'.
The end of the Spider-Verse Saga has the various incarnations of Spiderman reinspired to be better heroes and they thank him for it. In addition, Norman is fully cured of being the Goblin and in fact has all memory of the last few months wiped, meaning the Goblin within may be gone for good.