It may not be intended as such, but there are some cool ironic reversals of events in past incarnations. For example, we have Peter and Spidey "talking to each other" in a mirror, just like the scenes with Norman Osborn on the way to becoming Ax Crazy in the first film.
Also, Nick Fury's whole approach to Spidey. In the comic, Fury is very threatening and sounds downright evil, telling him that because he's a minor he can't touch him yet, but when you turn 18, "you're mine." Diplomacy, not his strong suit. In this version, Spidey's first meeting with Nick Fury has Fury pointing out the damage his battle caused, and telling him that with SHIELD's help, he could become a better hero, capable of solving problems more efficiently without anyone getting hurt. Spidey voluntarily joins SHIELD by the end of the series premiere. (He rejected it at first, but then he finds out that the bug the Trapster planted on him earlier led the bad guys to his school. Comes Great Responsibility did the rest.)
Harry being Venom makes sense when you look at how he was the Hobgoblin in the Ultimate comics. Both times are the result of an experiment, and both are a anti-reflection of another character, and Anti-Hero version his father in the comics and and Anti-Villain Spider-Man in the cartoon. It's essentially a way of getting the Hobgoblin storyline in without Norman having to be the Green Goblin yet.
It also works because Venom is the dark reflection of Spider-Man. What could be more dramatic than his dark reflection taking over his best friend?
While the Spider-Cycle doesn't really make a lot of sense, it is understandable why Peter likes it: he's 16 that's the age kids start to drive and become impressed by cool vehicles
Like how 616 Spidey briefly had a vehicle himself.
I just figured it was the show's version of the Spider-Mobile
And when it was introduced, They said it was a more efficient way to get around: Faster, and since it's SHIELD, no strained arms or using up expensive web fluid.
Why does Thor routinely defer to Coulson when he appears? Because this (sort of) shares continuity with the Marvel Cinematic Universe and Coulson is one of the few people that Thor knows, let alone trusts.
Remember in Iron Octopus when Norman said that Otto Octavius "perished in [his] arms"? In a very odd way, he was not lying-I mean, think about it. There isn't really anything to say that his personality wasn't altered at least partially due to the trauma of that accident...and then made worse by promptly being forced to shut himself away by the man he probably trusted a lot.
Despite all the complaints, Spidey fighting so many villains for other heroes' rouges galleries makes perfect sense: most of the Marvel universe is set in New York. How can a superhero who lives in NY (who web-swings, which is known to be a very speedy form of travel) not encounter so many other villains who run around causing trouble if it's all in the same city?
In episode "Venomous" Spidey's teammates are all too willing to hurt, beat, kill and destroy Venom, despite the fact that there is a completely innocent person inside Venom and that he is possesed by symbiote and is not in control of his actions, and they know that but they don't care. Granted, Spidey tells them that the person inside Venom is Harry Osborn and they are trying to stop Venom and free Harry from symbiote's control, but consider this: before they found out about Harry being Venom they were willing to kill Venom and did not care a bit that they might have possible murdered completely innocent person, who was not in control of his actions and was controlled by the symbiote, and despite knowing this, they didn't care. And what would have happened if Spidey didn't intervene...
In-universe for the Asgardian hunters in "Run Pig Run" once they realize the pig they'd been hunting and planning on making into their holiday feast was a human. Also, Skurge mentions mounting the heads of "other talking pigs" and after about a minute, Spider Ham says "...others?". The implication that Loki's carried out this plan before (and succeeded) is laid on fairly thickly.
Maybe they just have talking pigs on Asgard
"I am Spider Man" reveals Miles Morales exists in this show, so...
Yeah, because a Mythology Gag clearly means that the show is going to follow the exact same plotline of the comics, even though the whole premise of the show, that Spidey is part of a SHIELD team training alongside Iron Fist, Nova, Power Man, and White Tiger, didn't happen in the comics.