Adaptation Displacement: A character-only case. Karai's characterizations in the comic was very different than how she was portrayed in this series, but the latter got so popular this is usually what fans think about when the name of the character comes to mind, and all the other adaptations where she appears took from it in a way.
Author's Saving Throw: After Fast Forward was received negatively by a majority of the fandom, Season 2 was shelved and Back To The Sewers, which put the Turtles back into New York proper, was implemented. It didn't quite work, as some of the sillier aspects of Fast Forward followed and it was far more episodic, losing a lot of the intricate and complex continuity the series had.
Badass Decay: Bishop appears to suffer from this in Fast Forward, but redeems himself in "Day of Awakening".
Base-Breaking Character: Even to this day there's several fans who loved the twist of making the Oroku Saki Shredder the cover identity of Ch'rell and those who feel the cartoon royally screwed up by radically altering his character. There's also whether or not he was a cool villain and whose Arch-Enemy status to the Turtles was deserved or too overpowered and overly prominent, the latter of which probably isn't helped by a majority of the first three seasons conflicts eventually revolving around him.
Complete Monster: Ch'rell is a villainous Utrom, responsible for various crimes throughout the galaxy, including causing war on other planets which resulted in millions of lives lost. Captured by his normally-peaceful people, he caused their ship to crash on Earth, stealing the identity of the late Oroku Saki, aka The Shredder. Founding the Foot Clan, Shredder spent ages hunting down the Utroms and continuing his plans for galactic conquest. Upon finding the home of the Utrom's guardian, Hamato Yoshi, Shredder personally murdered him for refusing to give their location. Shredder's further crimes in the series include kidnapping random citizens to be turned into monsters for slave labor; executed a Purple Dragon member for failure; frequent physical mutilation of Baxter Stockman until he was reduced to a Brain in a Jar; and stealing the anti-gravity generator left in Beijing from the Triceraton invasion, ignoring Karai's protests that doing so will result in millions of deaths. Constructing a ship that will help him find the Utroms, he assaulted the Turtles and Splinter to near death for continuously interfering with his plans, then assaulted Karai for trying to stop him. After being imprisoned for his crimes, Shredder is freed in Turtles Forever.
Continuity Lockout: The series didn't adhere to Status Quo Is God, which resulted in a lot of long-running plot threads, major reveals that often end up casually conversed about, and bits of character development from episode to episode that people won't catch unless they watch avidly..
Crack Is Cheaper: Ever since Nickelodeon bought the franchise, they're more or less swept the 2003 cartoon under the rug. The DVD volumes and sets previously released by 4Kids have gone out of print, and good luck trying to get them all up to the Fast Forward season now: several of them go anywhere from $75 up to $200. While Nick has released DVD volumes of the 2003 show, these only have three episodes each much like the early 4Kids releases and are collected of random episodes, meaning the out of print sets are unfortunately still the best way to find them.
Draco in Leather Pants: Agent Bishop gets this treatment from a large portion of the fanbase. While he does change his ways and brings peace and stability to the Earth in Fast Forward, he still committed a lot of evil deeds in the bulk of his appearances, most notably attempting to dissect the turtles and Splinter multiple times, torturing Leatherhead, ruining the lives of his own men by mutating them into hideous monsters, and torturing countless sentient alien beings in the decades leading up to his ultimate Heel–Face Turn. Even though there's little doubt that Agent Bishop is a complex character and multi-faceted Anti-Villain who himself was experimented on by aliens during the Civil War and thus, has a sympathetic and believable motive for wanting to keep Earth safe from aliens invasions, a lot of his fans still have a tendency to play down all his evil deeds and romanticize him as little more than a noble and selfless Hero Antagonist who only has the best interests of the world at heart, even though many of his pre-Fast Forward actions show that he's NOT(most notably when he openly admitted to Splinter in "Bishop's Gambit" that he honestly doesn't care if innocent people get killed by his Slayers in his quest to root out aliens).
Franchise Original Sin: One of the bigger criticisms of later seasons is the Shredder tends to become the center of the conflict, often to the extent of pushing other, more interesting villains who were driving the plot up to that point out of the spotlight. In spite of this, Season 1 had this issue, with a number of subsections of the Foot Clan showing up, or revealing the villain of the episode had been working for the Shredder, but at that point, the Shredder was the only major antagonist in the series, so it wasn't as much a problem because most of the villains at that point lacked depth.
Fridge Brilliance: After his defeat in "The Shredder Strikes, Part 2," Shredder makes it a point of going after the Turtles and eliminating them. Seems like common sense and simple revenge, right? But then "Timing is Everything" showed Shredder after his first defeat facing the more-skilled Turtles by way of time travel. He knew they would become more powerful and eventually defeat him (as Raph says), so his motives weren't pure revenge.
Fridge Horror: Possibly mixed with Harsher in Hindsight. An un-produced episode of the Ninja Tribunal season was going to reveal that Hun and The Garbageman were conjoined twins separated at birth by a back-alley surgeon. That was horrific enough that it got the episode scraped by the network, but it gets even worse when who realize that it was hinted at two seasons earlier during "Same As It Never Was." Brings the Shredder's punishment of Hun and Stockman to an all-new level of "apropos."
In "The Shredder Strikes Back, Part 2" many of the Foot Ninjas are knocked out by the Turtles and Master Splinter, so when the Shredder blows up the shop (and by extension, the apartment above), it can be assumed that they perished in the resulting explosion. Although Stockman says in "Tales of Leo" that 'there's no conclusive proof to say anyone, turtle or human, perished in the fire', that still doesn't mean that all of the Foot Ninjas escaped the blast; it merely means that Stockman doesn't have enough data to prove it.
Growing the Beard: While Season 1 is good, Season 2 started putting greater focus on the characterization of the main cast, started to rely much less on the Foot Clan as a major threat in less plot-relevant episodes, and began to weave the story arcs that would come. Season 3 then followed it up with major status quo changes that affected the Earth as a whole, and giving the series more than one central villain, each with their own long-term plan and interesting characterization.
Harsher in Hindsight: An In-Universe example in Fast Forward. Serling has made a compilation of his home movies with Cody. There's lots of adorable, funny moments like Serling having to change Cody's diapers... and then we see a video of Cody getting patted on the head by a seemingly jolly Uncle Darius, who'd just been outed to him as a villain in the previous episode. The mood gets awkward, and Serling mumbles that he should probably remove that clip.
In "Exodus", it was promised "One of these characters will never be seen again.", and after the episode, Ch'rell is banished to an ice planet, likely never to be seen again... That is, until Turtles Forever, but even before that, Peter Laird confirmed that the Triceraton Shredder shown in concept art of a possible second Fast Forward season would have been Ch'rell hijacking the body of a Triceraton soldier, and Back To The Sewers not-so-subtly implied in its first episode that Ch'rell would fight the other two Shredders in the show (there would have been an arc called "The Shredder Wars"). Making the claim that Ch'rell would never be seen again hysterical.
On a similar note, there's this exchange, from season 5, before the Cyber Shredder was introduced (and, consequentially, before Turtles Forever and the whole 'Multiverse' thing).
Early on in season 1— the episode "The Garbageman"— Mikey tries out several catchphrases, much to his brothers' distaste. One of those catchphrases is "It's trench-coat wearing time!". Nobody (except the fans) seems to have a problem with "It's ninja time" five seasons later.
The Dark Turtles of the Fast Forward season have far more distinct designs than the Turtles, with Dark Leonardo having the most balanced physique, Dark Raphael having a bulkier form, Dark Donatello being taller and slimmer, and Dark Michelangelo being somewhat smaller than the rest. Barring Michelangelo, almost all of the design traits are exactly like the next incarnation's Turtles, who were all made distinct aesthetic-wise. Dark Raphael also has spikes protruding from his body and shell, which also makes him resemble Raphael's mutated pet Turtle Spike, who would become the next incarnation of Slash.
"The Return of Nano" has a bit of back and forth on Not a Date between Casey and April. During the climax, Donatello needs April's help for his plan and runs off with her, leading Casey to bemoan "that sneaky, little green nerd" running off with his date. This exchange got funnier in light of the three characters being in a love triangle on the 2012 show.
Baxter Stockman in the episode "Insane in the Membrane". Sure, he was an arrogant jerk, but we learn that he used to be a very sweet kid and in the present day breaks down after seeing hallucinations of his dead mother, which is made worse by his regret of never fulfilling his mother's dreams for her son while she was alive. It's especially hard to not feel sorry for him after he ends up dying after his new body completely decays and Bishop resurrects him, denying him a chance at finally dying in peace.
The con man in the first episode with Nano may have been using the colony of nanotechnology for his own ends, but as the episode goes on, he legitimately begins to care for him as if he was his son and even expresses remorse after Nano was seemingly destroyed.
Magnificent Bastards: The Ninja Tribunal. Can also be considered Guile Heroes since they are on the Turtles' side. Plus, the fact that they plan for the turtles to meet their destinies whether they are able to defeat the Demon Shredder or not is considered GOOD magnificent bastardom indeed.
The Heralds of the Shredder, a.k.a. the Foot Mystics, count as well for two of their successful plans; one to have Bishop free them by destroying the Heart of Tengu that allowed its user to control them, and the next one to resurrect their true master, the Demon Shredder, despite the failures of their demonic mooks.
Memetic Mutation: The fact that Leo rides a scooter and Raph knew how to knit are both still popular jokes among the fandom.
Moral Event Horizon: For the Shredder, this was the episode "Mission of Gravity", where we learned that not only is he willing to kill millions when it serves his purposes, he'd also do so when it wouldn't.
Nightmare Fuel: Baxter Stockman, especially the episode "Insane In The Membrane".
Shredder's reaction to Stockman's continued failures.
Same As It Never Was, the episode seemed to have been intentionally designed to be utterly terrifying, and probably to show exactly what the Shredder would do if he were to take over a planet, the results are, yet again, terrifying.
The Shredder trapping the Turtles, Splinter, Casey, and April in April's antique shop closet by setting the place on fire using the gas pipes. It set up a big two-part episode cliff-hanger for the show, which no doubt scared a lot of kids back in the day.
No Problem with Licensed Games: The first and second games (Battle Nexus) based on this series have a cult following, the latter especially thanks to its' challenging enemies, lengthy campaign, lots of replay value, tournament mode, and inclusion of the original arcade game. The third game was not quite as well received but still has something of a following.
Replacement Scrappy: The Demon Shredder. The Cyber Shredder is a borderline example, being a AI copy of the original with no really distinctive features on his own besides living inside cyberspace. The fact that his existence indirectly leads to the death of Viral is another black mark.
Stockman is hated for repeatedly cheating death. Also for being flat out arrogant, seeing the mutants in the show as "stupid animals", even though 2 of those stupid animals (Donatello and Leatherhead) are more intelligent than him and just acting condescending to anyone he deems to be intellectually inferior.
Starlee's family is rather annoying. Her mother is snobby and thinks of her species and planet as above others and acts rather rudely (she thinks Donatello is a criminal for wearing a mask, and asks if he's had his vaccination shots when he knocks everyone down to avoid getting hit by a laser). Her little brother, also messes with things he's not supposed to touch and gets away with it apart from Starlee yelling at him. It's not much of a surprise to see why Starlee didn't want everyone to meet her family.
The Ninja Tribunal, due to a majority of them being huge assholes who constantly manipulate their disciples.
Seasonal Rot: By Fast Forward, although some people would place it even earlier.
Really Season 4 was the high point with some complex and surprisingly well written arcs for both Leonardo and Michelangelo. The two retools made the show much more child friendly and typical (robots, digital realms, collect the clues saga), but Season 4 stands as a nice end to a good cartoon.
Season 5 is divisive: many people felt it did a good job wrapping up the remaining plot threads from the previous season, while others felt it was overly gimmicky and too much of an anime/Avatar ripoff, abandoning the series' original roots of being influenced primarily by the original Mirage comics.
Strawman Has a Point: Throughtout Season 4, Leonardo becomes increasingly hardened and more of a jerk than Raphael ever was. After the Turtles and Casey fail to stop a Purple Dragon convoy in "Dragons Rising," the trope is invoked as Leonardo delivers a pretty brutal "The Reason You Suck" Speech:
Leonardo: Half! We stopped half and only because we got lucky! Is that good enough for you? Is it?! We're always one step behind! We act like a bunch of amateurs! How many times are we gonna get beaten before you guys wise up and realize this isn't a game?! (storms off) Raphael: I hate to admit it, but he ain't wrong.
Tear Jerker: A few episodes. Especially any episodes involving Nano.
Kirby giving Donatello a sketch of him with a ray gun and final words: Don - "Life at best is bitter sweet." Take care of yourself. - Kirby
The stories in "Tales of Leo", especially Raph's which causes him to shed Manly Tears. When Leonardo recovers, Splinter sheds a few tears, too.
"Bad Day:" The Foot Mystics trap Splinter and the TMNT in a nightmare in which Klunk, April, and Casey all die onscreen.
All of the future Turtles' deaths in "Same As it Never Was." Particularly Raphael, where after he's fatally wounded crawls to Leo's dead body so he can at least die next to his brother.
The turtles' Heroic Sacrifice in "Exodus" - "It's all right, father, we're all agreed." They're just so quiet and resolute about it. Even knowing they'll be rescued at the very last minute doesn't soften the blow, particularly when you take into account that, while Raph, Don, Mikey and Master Splinter recover physically and psychically well enough, it later sends Leo in a spiral of PTSD that's just as heartbreaking to see because he just couldn't save his family.
The entire 2003 series got accused of this by fans of the '80s cartoon, with complaints that they wished it was more like the "original" series. The irony being that the 2003 series, was far more faithful to the REAL original Turtles of the comics, than the '80s series ever was. It was hit with this even more in Japan, where they were more fond of the 1987 Turtles.
Shredder being an Utrom. Good god, people raged at that back in the day.
Of the many complaints Back to the Sewers had, one of the biggest was the change in art style compared to the first six seasons.
Or characters, in this case The Dark Turtles. Mostly due to their subplot being dropped to make way for Back to the Sewer. Dark Leo's time with the turtles in their final appearance suggested the four had a chance to turn good at some point, but this would never come to pass.
The Rat King's appearance in "I, Monster" hints he'll reappear, but afterwards only cameos in the finale to Back To The Sewers.
They Wasted a Perfectly Good Plot: Some of the ideas in Back To The Sewers, such as the one-year Time Skip and Hun having founded his own relatively successful criminal organization finally independent of the Foot, could have had interesting ramifications if they were properly explored.
Unpopular Popular Character: To the Turtles, Splinter, Leatherhead, and many protagonists in modern times who know of his existence, Agent Bishop is hated and reviled, and for good reason, based on the number of times he's tortured them, kidnapped them, tried to dissect them, and generally made their lives miserable. Even in Fast Forward when Bishop has finally made the turn from villain to hero and is popular with the general populace, the Turtles still have an abrasive relationship with him at best, with Raphael in particular usually making snide remarks and taking verbal jabs at Bishop. To a lot of fans, however, Agent Bishop is bar none THE best character created for the show and has gone on to become perhaps the most iconic villain of the TMNT franchise not named Shredder. Him being a big enough hit with the fans was such that his character eventually became a Canon Foreigner to the IDW Comics and the 2012 TMNT show.
Values Dissonance: Jammerhead refers to the Turtles in "Playtime's Over" as "buggers" - whilst this is no more offensive than 'jerks' or 'boneheads' in America, in the UK this is quite a rude word, and not one you'd expect to hear in a children's show.
Villain Decay: Inverted, the Shredder managed to stay a dangerous antagonist, he even managed to top himself in every evil plan he committed, with the Utrom Shredder being considered the most dangerous of the bunch.
Zig-Zagged with Hun. While his fights with the Turtles become increasingly more one-sided, he becomes much more effective as a crime lord and even manages to get the Purple Dragons out of the Foot Clan's shadow in Season 4, pulling off at least two on-screen successful, coordinated robberies, although this diminishes a bit by Back To The Sewers, where he's played more for humor.
Karai suffers this badly in season 4. From one appearance to the next, she goes from destroying the turtle's lair, all of their vehicles, and nearly killing 3 out 4 turtles and Splinter to playing and losing a rather humiliating game of keep away for a McGuffin against Leo and Mikey, including a sequence where they pick her up and drag her by the legs before throwing her out of an elevator shaft, in a manner more suiting Bebob and Rocksteady.
The Cyber Shredder's plans are more petty and by-the-numbers than Ch'Rell's in Back To The Sewers, and due to the nature of Cyberspace, the Turtles manage to combat him far more easily when they meet him. He gets a bit of a second wind in "Wedding Bells and Bytes", coordinating an attack on the Turtles and all of their allies at Casey and April's wedding.
To recap, in Nano's first appearance, it's defeated by getting dropped into a vat of molten steel, and survived, only to get broken into pieces when it returned. An AI that's only a child at heart and doesn't fully understand right from wrong gets defeats more painful than what the villains in the series endure.
Nano's father figure Harry the Pick-Pocket is also a little bit sympathetic. True, he mainly went along with Nano's delusions that he was its father so it could help him in his crimes, but at times he acted as if he actually cared about Nano. This is made especially apparent when he mourned Nano's demise in its debut episode and was overjoyed to see it alive and well in its second appearance.
Doctor Stockman is an unusual example of a Woobie. A fairly standard villain, it is only once we get to ‘Insane in the Membrane’ that the audience learns anything about Stockman’s backstory, with the flashbacks to his childhood revealing the trauma he went through as his mother died from an unknown illness. In addition, he is slowly mutilated by the Shredder throughout the course of the first couple of seasons, and whilst this typically elicits little sympathy from the audience due to his thoroughly vile personality, when he is brought back once again by Bishop in ‘Adventures in Turtle Sitting’, we discover just how much he wishes to be free of his horrible existence.
Stockman: Why couldn’t you finally let me rest in peace? WHY?
Donatello has had to deal with some of the worst experiences over the course of the show. He's been in a Lotus-Eater Machine where he's seen Angel die before his eyes, been transported to a Bad Future, where he sees all of his brothers die before his eyes, and learns that Master Splinter and Casey Jones are already dead, been captured and Mind Raped by the Triceratons, and been infected by a mutant virus that turned him into a mindless savage beast and nearly killed him. All of this to the most peaceable, kindly turtle of the team.
Though not popular, Serling is probably one of the biggest woobies. Most, if not all the fans hate him and in-universe, the other characters treat him like a slave sans Splinter and Cody, suffers bad luck which is sometimes caused by his buttmonkey status, while other times, his pain and suffering is deliberately caused by the turtles (i.e. trapping him inside a video game surronded by extra lives that look and act like the turtles). Honestly, it's a miracle he never tried to commit robot suicide.
The sheer fact that the writers seem to cause Leonardo the most emotional and physical pain out of any of the protagonists makes him a Woobie in the eyes of some fans. Throughout the course of the entire show he's typically the most likely to suffer a No-Holds-Barred Beatdown, teeter on the brink of death, experience Heroic B.S.O.D. and is even acknowledged in one episode by Michelangelo to shoulder the majority of the responsibility so that his brothers are free to be themselves. What's more, his near decline into Knight Templar-hood in Season 4 as he struggled to deal with Post Traumatic Stress Disorder left many fans yearning to just wrap him in a blanket and give him a big hug.
Poor Leatherhead! He's been flushed down the toilet when he was barely more than a hatchling, rescued and reared by the Utroms, only to be left behind all alone when they returned to their own world, manipulated and lied to by Baxter Stockman, buried beneath a pile of rubble, tortured by Agent Bishop, which has left him with parts of his personality he must work hard to control, pursued by a crazed hunter, believed he'd badly hurt/killed Michelangelo in a fit of rage. Don't worry: Mikey was fine, which left him consumed with grief and believing he was nothing more than a monster and worthy of death, and finally his good friend Donatello was infected by Bishop's mutant virus and turned into a mindless monster. Leatherhead did eventually help Stockman to develop a cure for the virus in time to save Donny, but he was obviously deeply upset to see Donatello that way, and to be initially unable to help him. He may be one of the biggest and strongest heroes in the show, but it seems like just about every time he appears he's suffering from some kind of mental or physical anguish.
The Fugitoid/Professor Honeycutt: really depends on whether you find his personality + voice annoying or endearing.
One time character T9581. He started life as a human, got married and had a child, only to be mutated by Bishop into a hideous monster with apparently no way of communicating his feelings or intentions, was locked away in cryogenic stasis only to be freed by the Purple Dragons, who started to attack him, escaped from them only to be attacked by Leo and Casey who mistook him as dangerous, and then was attacked by Bishop and seemingly blown up. Although he escapes, he has no way of returning to his former life or family, and the last shot we see of him is the poor creature clinging to a buoy, gazing sadly at the gazebo where he got married. His whole story is a really tragic Tear Jerker.