Accidental Aesop: Every time the show hands us a lesson about great power and responsibility and the right thing in conjunction with Peter's keeping his identity secret, it ends up telling us that secret identities are a stupid idea and nothing good can ever come of them. Which is more or less true, if largely inapplicable toour daily lives.
Complete Monster: Green Goblin, Norman Osborn, is the maniacal mastermind behind many of the series' villains, and the most personal and wicked foe Spider-Man ever faced. When first revealing himself to the world, Goblin attacked a charity event hosted by his rival Tombstone, and quickly showed his penchant for sadistic overkill by setting a bomb to blow up and "paint the (ballroom) red" to kill Tombstone, taking sick joy from the fact it will kill the dozens of charity-goers and his own men in the process. After instigating a gang war that consumes nearly an entire city block so as to eliminate his competition, Goblin proclaims himself the new "Big Man" of crime, brutalizing and possibly killing any who stand against him. Goblin's grandest and cruelest plan came when he set booby traps of bombs across New York City in an insane attempt to kill Spider-Man, uncaring of the countless innocents that could be killed. Goblin also has a penchant for creating supervillains to serve his purposes, be it subjecting the meek Otto Octavius to a lethal experiment that turned him into the sociopathic Doctor Octopus; turning the young Mark Allen into a Man on Fire to force him into servitude; and takes full part in the creation of Sandman and Rhino, using them as guinea pigs to deadly experiments. As Osborn, he verbally abuses and neglects his teenage son Harry, finances and funds various criminal and supervillain enterprises, and framed his own son as the Green Goblin, severely injuring the boy's leg to complete the set-up. Be it his supervillain or public persona, Green Goblin was a consistently depraved monster, with a lust for power being the only thing driving him.
For many fans, this series is to Spider-Man what Batman: The Animated Series and Superman: The Animated Series (it also ran for two seasons with plots left hanging without a renewalnote It eventually got resolved via the very popular Justice League but before that the executives insisted Batman Beyond come first and even then we never see Clark reveal his identity to Lois in the show, even though she and Superman start a relationship) are to their respective franchises. An Adaptation Distillation that honors multiple iterations of the character, and with good writing skilfully balances the humor, seriousness, romance, and genre elements with excellent voiceover work that has Multiple Demographic Appeal.
Comparisons between Spider-Man and Harry Potter are dime-a-dozen, but this show really makes it obvious. Originally, Peter's part of a Power Trio, being a socially awkward Hollywood Nerd orphan, with his best friends being a bookish but sincere girl (Gwen Stacy/Hermione) and his best friend being a freckled red-head who is perennially envious of his friends and peers about being Overshadowed by Awesome (Harry Osborn / Ron Weasley). Peter's also has a rivalry with a haughty blonde jock (Flash / Draco Malfoy) and later catches the attention of a vivacious redhead who is Fun Personified (MJ/Ginny), and the series' main villain is a man who disguises his identity and actions through subordinates and likewise fakes his death (Green Goblin/Voldemort).
J. Jonah Jameson. Daran Norris nails it, making Peter's ill-tempered boss hilarious.
Gwen's portrayal is one of the major reasons for her surprising resurgence in popularity. Her design (especially since it becomes closer to her comic counterpart's own) and voice are very, very adorable and she's got a Cool Big Sis dynamic with MJ. Though her film incarnation is particularly different, she's the other half of the reasoning. When it's not her, fans tend to think of this version. The Spider-Gwen comics seems to split the difference between the two.
Green Goblin either in costume or as Norman is a frighteningly competent, dangerous adversary who is Laughably Evil while Norman is the unflappable The Man Behind the Man, having the best qualities of both Lex Luthor and The Joker, simultaneously, in a way that even his comic book counterpart hasn't quite pulled off.
Hammerhead is quite interesting as a middle-man for Tombstone and (later Goblin) who shows some Evil Virtues (namely loyalty, perseverance) and the animation where he goes into his famous headbutting move is genuinely cool and compelling. Add in that he dresses like a classic '30s gangster (complete with vintage car), and you have a memorable minor villain. The fact that he and Silver Sable are exes makes him pretty interesting.
The Sandman gets this especially in his last episode where he really shows off his powers by attacking an oil tanker in the ocean and does by converting himself into a moving sandbank (lampshaded by the ship captain noting that the beach is coming to them), and the battle with Spider-Man features an entire forest of fists jutting out of the ground, showing the true potential of his powers in a way that Spider-Man 3 didn't do. The fact that he reveals heroic qualities by saving some of the sailors in that attack only makes it cooler.
The Alien Symbiote, especially when it becomes self-aware and fights the entire Sinister Six by itself and wins, and then provides Peter a Battle in the Center of the Mind that is genuinely compelling and suspenseful.
Primarily with Spider-Man: The Animated Series and Ultimate Spider-Man. With the former, fandom got into nasty arguments over which is the "definitive" animated Spider-series. With the latter, Ultimate was Disney's replacement series for Spectacular.
And now a similar rivalry is starting to form with Marvel's Spider-Man, with many Spectacular Fans bashing the show after its first short and complaining that their favourite adaptation still isn't coming back.
The entire Symbiote arc. Venom—or more accurately, the symbiote itself—acts as a spurned ex/stalker towards Peter Parker. Eddie Brock doesn't seem to have much issue with this either, judging by all of those unsettling leers aimed at the web-head. Of course that could just be the symbiote's influence, but it's certainly there regardless. The symbiote doesn't seem to have any problem going on about how much it just wants to be with Spider-Man. Spidey even refers to himself (albeit somewhat ironically) as its "first love" at the end of "Nature vs Nurture". Venom seems to hate Spider-Man just as much as it wants him back/to itself.
Norman Osborn's obsession with Peter Parker already borders into Ho Yay territory (not that Peter helps matters, Normie-kins indeed...), but Spider-man and the Green Goblin?
The first five episodes are entertaining; however, episode six abandoned the usual "two fight" format, going for one big fight with The Rhino instead, and then introduced Tombstone.
Season two also introduced much more complicated, long-running plot threads and twists, and generally amped up the quality of the fight scenes, which were already arguably amongst the best of Western Animation as is.
Ham and Cheese: Mysterio, who milks his sorcerer shtick for all it's worth. As Tinkerer mutters, "Actors"
Hype Aversion: Unfortunately, the fandom has caused this, due to their boasting that this is absolutely the best Spider-Man adaptation ever and not accepting any other opinion, as well as their consistent (and often times unnecessary) bashing of Ultimate Spider-Man and its fans have scared off a lot of people who missed this show, and caused them to not want to watch it, either due to disliking said fandom's attitude or feeling it won't stand up to the sheer amount of hype and praise surrounding it.
Just like in the comics, Harry is this. He may have ditched his friends when he was In with the In Crowd and manipulated Gwen into staying with him, but given how his home life is and how he's treated in general, you do feel sorry for him while.
Les Yay: Mary Jane and Liz in "Subtext", particularly in the last scene when they are performing their lines for the play to one another - even the episode's title adds to this feeling. For all anyone knows, MJ and Liz were each other's rebounds after the show ended! It certainly adds another dimension to MJ's "Finally!" line in the last episode.
Magnificent Bastard: Tombstone, Dr. Octopus, and Norman Osborn. Their schemes run rings around every other character in the show. Ock is to the point that his in-universe title is the Master Planner, and Spidey spends a fair few episodes just trying to find out who the heck the Master Planner even is!
Norman framing Harry solidifies him as an amoral bastard, but injuring Harry's leg to do it demonstrates a casual cruelty and cowardice that erases any hint of redemption. Though manipulating Mark Allan was also up there.
Venom crosses it by revealing Spider-Man's identity in the first place knowing that he and his loved ones will be threatened.
Narm: Eddie Brock, post-Venom, in his moments without the symbiote.
Twas the night before Halloween, and all through Manhattan,
Not a creature was stirring, not even Green Gob...lin.
Paranoia Fuel: Eddie Brock uses this to make Peter reveal the location of the symbiote, allowing him to become Venom once more.
Periphery Demographic: Many of the show's fans appear to be adults. This is most likely because Greg Weisman was working on it, who has many fans that were children when Gargoyles came out and by the time Spectacular was created they have grown up. The top-notch writing and fight scenes don't hurt either.
Rewatch Bonus: After Peter gets the symbiote, it starts speaking to him (in his head). You won't realize this until Pete does.
For some, Mary Jane Watson. She was built up a good deal before her introduction in episode 6, and then showed the makings of a great supporting character and potential Love Interest for the rest of Season 1. But in Season 2, MJ is regulated to being Gwen's Cool Big Sis figure who's a Shipper on Deck for Gwen and Peter, and is only a focal point of a subplot centered on Marc Allan. The series was cancelled before her role could ever expand, so she comes off as an underwhelming waste of potential for a character who's been established across other media as the love of Peter Parker's life. Greg Weisman and his writing staff might have wanted to replicate the slower build towards the Peter/MJ romance from the original comics, but many feel that sort of slow build didn't pan out well in this medium. Others, who are fans of Mary Jane Watson appreciate the series however for portraying her just like how she was originally portrayed in the comics (along with getting her personality right, and for her being a genuinely good person, and for averting the Damsel in Distress that the Raimi movies affixed on her).
Many felt that the Alien Symbiote was a more interesting villain than Venom and Eddie Brock. Many lamented the fact that given how the show is trying to be Truer to the Text, that the showrunners didn't go with the original ideas for Venom (where the Symbiote was the main bad guy who would periodically latch on to other hosts, drain it and move on vampirically and Eddie Brock was never intended as the final or only host) and instead went with Eddie Brock as a host, for legacy reasons.
They Wasted a Perfectly Good Plot: When John Jameson has difficulty in space and all of Earth is transfixed by it, Randy Robertson is particularly worried and says that John is "like an older brother to him". Given that their fathers (J. Jonah Jameson and Robbie Robertson) work closely together, this relationship makes perfect sense. However, nothing more of it is ever seen or spoken of, even after John is driven insane. It seems like in juggling the Loads and Loads of Characters in this show, the ball was dropped on Randy.
Peter Parker, during his relationship with Liz Allan. He doesn't even attempt to hide that he has feelings for Gwen (or doesn't even realize he shouldn't be making it that obvious) even when right in front of Liz. Not to mention he and Gwen deciding to break up with Liz and Harry at the end of Season 2. This is coming right after Peter spent all season not showing up to his and Liz's dates (admittedly for crime-fighting), showed favoritism to Gwen over her on Valentine's Day, and Mark Allan's arrest for supervillain activities. Not to mention the fact that Harry was kidnapped by the Green Goblin and a struggling addict who had his secret outed by Flash a number of days prior.
In fact, they decide to get together just minutes after Harry tells them that he's spent the last several days kidnapped!
Also, his attitude towards Dr. Connors; when Connors became the Lizard, he took a picture of himself fighting Lizard, making it look like he (as Peter) had been hiding and choosing to do his photograph job over helping Connors. Now, this could be forgivable as a one-time mistake, but he does it again in Persona, when he takes pictures of his fight with Black Cat over the symbiote, making it look again like he couldn't even bother to call the police. Even worse, Brock actually told him he couldn't take pictures right before precisely because of the trust issue.
WTH, Casting Agency?: Tinkerer's voice makes him sound like a child, when he's supposed to be an old man. It's obvious that the voice was misused, since years later, Adcox would indeed use the same voice when cast as a child. However, that's Adcox's actual voice, and he's about as old as Tinkerer.
True to the comics, the sheer amount of crap poor Peter Parker and Spider-Man get put through over the course of this show is unbelievable.
Liz Allan has an elder brother who did time in juvie and has a gambling addiction, and deals with this problem on her own with only MJ for support, since Peter, as he himself admits has been a terrible boyfriend to her, being both neglectful and emotionally unfaithful to her since he blatantly favors Gwen in public over her.
Both Liz Allan and Gwen Stacy by the end of the series. Liz is left brokenhearted, having recently lost her brother and then losing Peter as a boyfriend. And Gwen really wants to be with Peter but is emotionally manipulated and guilt-tripped into staying in a relationship with Harry Osborn.