"Why I Hate Gym" has a scene where Taskmaster, in an attempt to convince Spider-Man to join him as his apprentice, reveals he used to work for S.H.I.E.L.D. as well, but left after Nick Fury double-crossed him. Having Spider-Man questioning his trust in Fury, and considering quitting because of this, could have been a great plot device that would have brought Character Development to the three characters. But the episode instead focuses on Spidey and White Tiger trying to find a way to defeat Taskmaster, and Fury's double-crossing is never mentioned again.
And this isn't an isolated case; so far, Fury has been hinted to be responsible as well for both Scorpio (actually his brother Max) creating Zodiac and Sandman ending up nuts after he trapped him alone on an island for years. He never gets called out for his actions, and neither Spider-Man or his friends seem concerned with it.
The entire premise of the show. Spider-Man teaming up with other heroes could have worked great as Marvel's equivalent to Batman: The Brave and the Bold, but it ends up defeating the purpose by having him on a single team of jerkasses almost every episode and sometimes having him act like an annoying, incompetent idiot. If this show had taken place later in Spidey's career when he's a full-grown adult whose faced multiple villains, as well as having him team up with one hero each episode, this could have been the animated equivalent to Marvel Team-Up or Avenging Spider-Man. Although around season 2, this did end up changing for the better as the characters started to be better written. It's just by season 3, the focus drifted away from the starting five to other characters.
The episodes Carnage and House Arrest tease us with the possibilities of Harry, Green Goblin and Aunt May finding out Spider-Man's secret identity, only to not follow through with it. Never mind the fact that both Harry and Goblin knowing is a big part of the mythos and while Aunt May only knew for a relatively short period of time in the comics, many considered that to be one of the better decisions Marvel ever made with her character.
Well, we did eventually get Goblin finding out from Peter Parker's tombstone in another universe, Peter revealing his identity to Harry to save him during the Symbiote Saga, and Aunt May having known the whole time, so I guess it did set it up. (Man, seeing all of these written before certain events in the show is so weird in hindsight.)
Norman Osborn's redemption story arc as Iron Patriot actually was pretty well-received and liked by the fans. It lasted around an episode, only to have Norman being turned back into the Goblin for the season finale.
"Damage" has the team working undercover at Damage Control, trying to figure out why the Wrecking Crew just showed up, busted a few city blocks, and ran without stealing a dime. Everyone besides Spidey gets turned into an idiot or an adult who just doesn't listen when kids talk, including Nick Fury, who assigned them to this job at least in part so they could figure out what happened. Arguably Nick was more interested in giving the young hotheads some humility by having them engage in manual labor, but it was at least ostensibly an undercover op. "Undercover" in this case means "present in their superhero identities but wearing Damage Control jumpsuits", And since J. Jonah Jameson is still JJJ, he gleefully puts his cameras on Spider-Man being forced to do drudge work and broadcasts it. "Undercover." Right. Although one supposes some leeway must be given, as they clearly don't have character models for what the team looks like outside of their costumes...
The Spider-Verse Arc. One might argue it's an improvement for actually being about Spider-Man and not shoehorning in his "friends", but fails for several reasons. First off, we barely get a chance to get to know these alternate Spider-Men since each episode is just 11 minutes of one world twice. Second, most of them suffer the same problem (Feeling like they should give up only for our Spider-Man to convince them not to). Third, the entire plot was so Green Goblin can steal spider-DNA to use on himself, ignoring that his Goblin formula was made from Spider-Man's DNA and this Spider-Man has had his DNA taken rather easily before. In essence, this was just advertisement for the comic book event, which had an actual reason to involve alternate universes.
In the actual Ultimate Comics Peter's parents were friends with Nick Fury, and their most common origin (both in the Ultimate Universe and the main, 616 one) tends to be that they were secret agents of some sort. This could have been an amazing plot point in the first season to play around with, and they could have used it to develop an interesting, complicated relationship between Spider-Man and Fury, but absolutely nothing has been done with this and the show is going into its fourth season. Not even in season 3 where Taskmaster (who clearly has something against Nick) reappears and starts to try and make his own team. This could have caused tension between Fury and Spider-Man that they'd have to resolve, rather than having the viewer sit through several episodes that could be perceived as filler.
Oddly of the superheroes that show up in the series, Ms. Marvel aka Kamela Khan wasn't one of them which is weird considering she's a teenage superhero herself and was gaining major promience when the show was running (Heck they manage to get Amedeous Cho by season 2, Miles and Agent Venom in by 3 and Spider-Gwen by 4) so you'd think that would make her a perfect candidate for Fury's school of heroes. Many had expected her to least show up in season 4 but nope. Rather she made her offical animated debut in Avengers Assemble with another team. This would be rectified later with Marvel's Spider-Man where she shows up in season 2 and becomes something of a recurring character in that series by season 3.
One of the most awesome things to happen in ANY version of Spider-Man: Mary Jane gets taken over by a symbiote queen, corrupted into an Arc Villain, gains control, and becomes an honest-to-goodness superhero - a good version of Carnage, no less! Significantly less awesome is all this happening toward the very end of the series, and her only getting to be a superhero for three episodes.
