All Love Is Unrequited - Bobby and Peter both have romantic interest in Angelica. Whether she returns it for either of them is not really explored.
Bobby and Peter did discuss this in one episode: Bobby said fire and ice don't mix while Peter was worried that if he made a pass at her and got rebuffed, it would mean the end of the Spider-Friends.
Near the end of the series, Peter and Angelica had gone on a few dates. She was also visibly heartbroken in an episode where Peter falls hard for, and elects to go home with, a woman from the future whom he'd basically just met.
Alpha Bitch - Bonnie, the girl who gave Angelica her "Miss Angelica Jinx" nickname in "A Fire-Star is Born".
Animation Bump - The three-episode second season was animated by Toei, and the animation and character models became more detailed and fuller, with a greater use of underlighting special effects. Incidentally, all three episodes deal with Iceman's, Firestar's, and Spidey' origins
Arbitrary Skepticism - The Spider-Friends are okay with believing in mutants. Mind control. Evil potions. Bees from outer space. Shapeshifting. Dracula. But that Thor is actually the Norse god of thunder? No way...
Arson, Murder, and Jaywalking: In "Spider-Man Unmasked!", Peter has a nightmare over what the fallout of his identity being revealed would be. He sees Sandman gloating, Aunt May crying and finally Jonah.
Angelica (referring to Ms. Lion): Well, somebody's found a friend.
Peter: You can say that again!
Angelica: Her name is Ms. Lion. I'm Angelica.
Peter: You sure are... I'm Peter Piper... Uh, P-Parker... Uh, Parker Peter-
Dramatic Unmask - The episode featuring an explanation of how the Spider-Friends formed has Spidey taking off his mask to reveal his true identity to Angelica and Bobby since Peter figured out they were Firestar and Iceman, respectively.
Easy Amnesia - In "Video-Man", Flash Thompson figured out Angelica Jones is Firestar. A bump on the head made him forget it.
Evil Former Friend: Firestar's old friend Nathan Price became Cyberiad due to an accident caused by A.I.M. terrorists. He blames Firestar for what happened and wants revenge. But a part of him still cares for Firestar, while Cyberiad just wants to destroy her.
Fiery Redhead: Taken almost as literally as one possibly can with Firestar.
Gag Dub: The original (late 80's) Mexican dub inserted tons of jokes (inside ones such as substituting Stan Lee with his 'granddaddy' when that voice actor was unavailable), hamming villain with silly phrases (Magneto has never been funnier) and tons of adlibbed extra lines.
Just the translations of the names of some characters could crack you open, you have Dinamyc needle and Draco Dragoon instead of Wolverine and Daredevil...but somehow you still have Juggernaut untranslated.
Getting Crap Past the Radar: Bobby calls Peter a "buttface" after Peter, in a rush to get his Spider-Man costume out of the washing machine, wakes Bobby up from dreaming about Angelica.
Spider-Man also pulls it off with an unwitting Flash Thompson, in the episode where the Sandman tumbles upon Spidey's Secret Identity.
Similarly, Dr. Zoltan Amadeus uses science to replicate Spider-Man's powers, then dresses up as him to commit crimes that Spider-Man is then blamed for. Unfortunately for Zoltan, the formula he used to gain those powers is unstable and winds up mutating him into something more spider than man. Eventually he doesn't even care since he's become very powerful.
Implacable Man - The Juggernaut during his appearance in 'A Firestar is Born'.
Jekyll & Hyde - In the comics, the Green Goblin is just a costumed identity that Norman Osborn assumes; in the series opener, Osborn physically transforms into a green-skinned creature. (No, not that one.)
Never Say "Die" - Subverted. In The Eighties, it hadn't yet become unfashionable. Not only did the word "kill" get used, but a scene implied onscreen that Spider-Man had been killed in battle before pulling a "gotcha!" on the viewer.
No Swastikas - Averted with the episode of "Quest of the Red Skull", in which the heroes team up with Indiana Jones expy/American Indian shaman "Hiawatha" Smith to stop the Red Skull and a pair of German-accented minions from finding a horde of Nazi plunder and secret superweapons in the South American jungle. A shadow-casting stone swastika is even the key to finding the entrance to the stash. Smith gets pretty Anvilicious about the evils of the Third Reich. Of course, itisthe Nazis he's talking about. A bone is throw to the pre-Nazi history of the swastika when one of the Skull's minions mistakes a Native American tapestry design for a swastika. He gives it a "Heil Hitler" upon seeing it, though is corrected by the other minion immediately.
On the Money: The episode "Spidey Goes Hollywood" has Spidey agreeing to act in a movie for the exact amount Aunt May needs to pay the mortgage this month (as opposed to say, enough to pay off the whole mortgage).
Then again, unless Peter is willing to tell Aunt May he's Spidey, he'd probably have to come up with some excuse to justify suddenly having that much money.
The Other Darrin: While 2 Spider-Man cartoons aired at the same time (This alongside the 1981 Spider-Man Animated series), Spider-Man and his Amazing Friends featured Dan Gilvezan as the voice of Spider-Man, as opposed to Ted Schwartz (Who voiced Spider-Man in the 1981 Spider-Man Animated Series)
Averted for the character of J. Jonah Jameson as William Woodson voices him in both Spider-Man cartoons.
Origins Episode: "The Origin of the Iceman," "Along Came Spidey", and "A Fire-Star Is Born" for each of our Power Trio. "The Origin of the Spider-Friends," meanwhile, unsurprisingly explains how they met and formed their team.
Secret Keeper: In "The X-Men Adventure", Professor X learns of Spider-Man's identity, but swears he won't reveal it. To Spider-Man's relief.
Sir Not Appearing On This Cover: The thumbnail on Netflix has a full-body shot of Spidey, but Firestar and Iceman got cropped out except for a few of their limbs.
Snow Means Cold - Spidey and Iceman first met during a Let's You and Him Fight situation. Iceman got Spider-Man's attention by causing a freak blizzard during the summer. Iceman wasn't seen actually throwing snow around to do it, but appeared to be just willing it to happen.
Stan Lee - narrated the series. "Excelsior!!" (Though many of his narrations were not on the masters used for the ABC Family showings and the masters were kept for the later Disney XD airings and Netflix release.)
Viewers Are Morons - The comic book Iceman is brunet, but he was rendered blond for the show because it was believed viewers wouldn't be able to tell Bobby from Peter if both were brunet. They also gave Flash a different shade of blonde, since Bobby resembles Flash.