Bowdlerise: The ABC Family run of the show heavily censored several episodes for being Too Soon due to 9/11. Some episodes were even completely taken out. Thankfully, later runs on the channel (as well as it's run on Toon Disney) would be shown uncut with all episodes intact and shown.
The writers weren't allowed to use the words death, die, or kill; hence, when Peter found out Uncle Ben had been killed, it was shown as a police officer shaking his head and saying "I'm sorry, kid. The guy was armed." Also, realistic guns were out, so even petty thieves were armed with futuristic lasers.
A case of executive meddling having an outright odd effect was in the character of Morbius, a vampire. The writers weren't allowed to show him sucking blood through his fangs, so he apparently has fangs for no reason, as he instead drains plasma (they can't use the word "blood" apparently) through suckers in his hands. The suckers were so squicktastic that they made the character even creepier, whereas his declarations of "I hunger for PLASMA!" were often Narm. Interestingly enough, the Swedish translator had him hungering for blood plasma.
Another example is Carnage. In the comics, he was a mass-murdering psychopath, but in the series he wasn't allowed to kill anyone — instead he sucked out their "essence" through his hands, which was restored to his victims after he was sucked into a portal. In the scene where he acquires the symbiote he attacks some prison guards; he picks one up and makes some knives with his fingers but instead it shows him busting through a wall. In all fairness to Fox, the NYPD's description of Cletus Cassidy implied his psychopathic tendencies, not to mention his mannerisms and laughter were still pretty creepy in their own right (especially the laughter). So while Carnage could not kill anyone, the censorship didn't stifle his sadistic personality.
Spider-Man was also never allowed to throw a punch because it would make the show too violent. The writers managed to slip just one punch in the 65-episode series. Although Tropes Are Not Bad in this case, as it forced Spider-Man to be much more clever in his crimefighting, which fits his genius-level intellect.
They also weren't allowed to break windows, which also got snuck in, one wonders how they missed that.
If that's not absurd, listen to these:
"When Spider-Man lands on a roof, make sure he doesn't harm any pigeons."
"Spider-Man can imprison a villain, but they can not be given a ticket to California to leave."
Another positive effect occurred when the writers were forced to introduce the Hobgoblin in season one rather than the Green Goblin, to match the toys that had been ordered. This allowed Hobgoblin to become an engaging character in his own right and a precursor to the more dangerous Green Goblin.
The censorship standards led to The Punisher being pretty much castrated. He was purely non-lethal and pretty ineffective as a result. However, the telling of his origin (for those unaware, the brutal shooting of his wife and young children which obviously couldn't be shown) was incredibly effective. The only visual was a kite flying in the sky and at the sound of gunshots fell to the ground, landing in a puddle and forming the classic skull as it became soaked in water.
Why Sandman never appeared and Electro was an altered character. When the series started, James Cameron's movie was going to feature the two as villains (though with heavy tweaking), so the rights were all tied up. (The reason why Electro was snuck in towards the end was because by that time it was a given that Cameron's project was never going to happen.)
Mark Hamill brought what was essentially a slightly deeper, more toned-down version of his Joker voice to the Hobgoblin, but it works very well.
Spider-Man himself, Christopher Daniel Barnes, was well-known for playing Prince Eric in Disney's The Little Mermaid and would later play Greg Brady in the first two movies which parodied the Brady Bunch as well as Prince Charming in the direct-to-video Cinderella sequels. Twelve years after the show ended, he voiced Noir Peter Parker in Spider-Man: Shattered Dimensions and is voicing Miguel O'Hara in Spider-Man: Edge of Time.
Hank Azaria (Venom/Eddie Brock) is better known as... Moe Syzslak, Professor Frink, Apu, and countless others from The Simpsons.
James "Uncle Phil" Avery reprises the role of War Machine from Iron Man season 1, and Dorian "Season 2 War Machine" Harewood is Tombstone. In fact, with the exceptions of most of the Fantastic Four (Quinton Flynn did return as the Human Torch, though), Doctor Doom, and Daredevil, pretty much most of the voices actors from the other Marvel series at the time reprised their roles on the show. However, Tom Kane voiced Doctor Doom.
I Want You to Meet an Old Friend of Mine: Christopher Daniel Barnes, who provided Spider-Man's voice, and Robert Hayes, the voice of Iron Man, had previously starred together in Starman. Both were reportedly thrilled at doing a team up.
Missing Episode: Following the 9/11 attacks, ABC Family pulled "Shriek of the Vulture" and "The Final Nightmare" (both of which featured a burning skyscraper) from the rerun schedule. These two episodes concluded the Neogenic Nightmare arc and led into Season 3's "Doctor Strange", so you can imagine how displeased fans were. It wasn't until the end of 2007, though, that this changed. Toon Disney aired the two episodes as a part of an all-series New Year's Eve/Day marathon. As long as the show has been airing, the two episodes have been rerun regularly ever since.
Mythology Gag: In the Grand Finale Peter visits another universe where among other changes from his own universe Mary-Jane is a shallow empty-headed party girl unlike the Mary-Jane he knows. The amusing part is the shallow empty-headed party girl WAS her character when she was introduced in the comics before Character Development that this show had skipped in order for her to be the Betty to Felicia Hardy's Veronica.
The Other Darrin: Richard Moll replaced Martin Landau as the Scorpion. After the deaths of Philip Abbott and Linda Gary, Jack Angel and Julie Bennett replaced them respectively as Nick Fury and Aunt May. Oliver Muirhead (who'd earlier voiced the Spot) replaced Malcolm McDowell as Whistler. As noted earlier, despite most of the guests star retaining their VAs from prior shows, outside of Quinton Flynn, the Fantastic Four were recast, along with Daredevil and Doctor Doom.
Promoted Fanboy: Armando Coria, the Mexican voice actor who voiced Spider-Man in the Mexican dub of the series, is a hardcore fan of Spider-Man since childhood.
Role Reprisal: Quite possibly one of the most expensive use of this trope, as the voice cast of X-Men: The Animated Series was flown from Canada to Los Angeles for their voice recording session.
Screwed by the Network: Sort of...it's a bit complicated. The show was always intended to have 65 episodes as was tradition at the time but it was popular enough it could have received more episodes but the head of development for Fox Kids hated Avi Arad who was the producer for the show. Story Editor and showrunner John Semper has gone on record in saying the show ended the way he wanted to with Peter Parker saving all of reality, meeting his creator, and being content with his life and any further seasons would have just been doing it for the money.
What Could Have Been: The adaptation of Secret Wars was originally going to feature a number of additional characters, most notably Mister Sinister. These were later scrapped for numerous reasons — namely costs since Sinister's voice actor, Chris Britton, is Canadian-based (the cast of the X-Men series had previously been flown to LA from Canada for their appearance in the crossover, which proved expensive. Storm got to appear because she's a case of The Other Darrin, and her former voice actress was in LA.)
The first showrunner that John Semper replaced before actual production on the show started intended for Norman Osborn to become The Hobgoblin,which likely meant the Green Goblin never would have shown up! This was probably due to the Green Goblin being dead at the time the show started. When Semper came in it was too late too prevent the Hobgoblin since toys were already being made but he did rectify it by having Norman Osborn create the Hobgoblins weapons instead of being the Hobgoblin