Accidental Innuendo: "Donatello does machines!". Made even more hilarious by the fact that he's the only turtle without an official Love Interest. Though it's been implied that Irma does canonically have a bit of crush on Donatello in several episodes such as "Sky Turtles" and "Invasion Of The Turtle Snatchers", which means that he's really shy, or Oblivious to Love, unless he's actually Robosexual.
The end of the first act of "The Lost Queen Of Atlantis" has a freeze frame of Shredder taking a magic amulet off of April while she's being restrained, which from the angle of the shot looks like he's grabbing April's breastand maniacally laughing at the same time.
Adaptation Displacement: This is the version most people remember when they think about the Turtles (or at least most people in their mid-20's or older).
And even others are theorizing that her constant chasing after men (or, more accurately, anything male) is her way of covering up actually being a closeted lesbian, which leads us to:
April and Irma's friendship seeming to be one-sided. Irma always mingles with April, and even refers to her as her best friend, however, April doesn't necessarily seem to ever return the sentiments. On top of that, because Irma seemingly clings to April seems to egg on the above-mentioned closet theory that perhaps Irma wants more than just friendship with April.
The piece of music that plays when the Technodrome's on screen.
The Italian theme song. It sounds absolutely nothing like the original, but it's nice and surprisingly catchy.
Designated Villain: Baxter Stockman's worst crime (before turning into a fly) was helping out Shredder, but the way the Turtles treat him you'd think he killed their mom or something.
Thanks to Baxter and his rat-catcher Shredder nearly succeeded in killing Splinter and Baxter also pulled off a Dog Bites Back move where he easily defeated the Turtles and likely would have done so to Shredder as well if not for him not knowing the Eye of Sarnath's one weakness. Shredder may have easily been the more eviler of the two, but he definitely wasn't an innocent victim.
Draco in Leather Pants: Shredder has quite a few fangirls. Doesn't help that he's sometimes more entertaining to watch than the good guys.
Though Turtles Forever was meant to highlight the differences between the 2003 series and this one, so including the more serious seasons would largely defeat the purpose.
"Funny Aneurysm" Moment: One of the first episodes featured an entire building flooding out and spilling a massive amount of water in the city when said building explodes from the pressure. Though copious on its own merits already, it can hit way too close to home for those involved in the aftermath of Hurricane Sandy, especially since the setting for the cartoon is New York City.
Season Three, arguably, when compared to the somewhat lackluster Season Two. It wasn't consistently good, but contains the most fan favorites.
Season Seven, the last "normal" season, is considered to be the best of all, due to some surprisingly well-written and enjoyable episodes. "Night of The Dark Turtle" and "Legend of Koji" are believed to be the best episodes in the entire series.
Harsher in Hindsight: "Enter The Fly!" has Baxter and Shredder plotting evil on top of the Twin Towers. Yikes.
"Get Shredder!" has the Channel 6 building being blown up by a bomb, which became much harsher after the Oklahoma City bombing. Surprisingly enough despite this the episode was never banned from airing unlike episodes of other shows which featured similar scenes(I.E. "New Partners on the Block" in Bonkers).
Lotus Blossom was introduced in the cartoon a few years before Karai debuted in the comics.
An early episode has a toy company employee presenting "Trans-Farmers" which are toy robots that transform into farm equipment. Sometime in the mid-90s when Playmates was desperate for new ideas to keep selling the toys to kids, not only did they do various transforming versions of characters(mutating varieties as well as vehicles), but there were also farming turtles with tractors. I wish I was making that last one up.
Ho Yay: You have to admit, the way Shredder and Krang would bicker throughout the series made them look like an old married couple. May also count as No Yay.
James Avery himself even lampshaded this in his Under the Shell interview, saying he and Pat Fraley treated the interaction between Shredder and Krang like they really were an old married couple. When asked what Shredder was up to recently, James responds, in-character as Shredder, "Krang and I are divorced now, I haven't seen him in many years. I kinda miss him, but not really, he was always such a nag."
Bebop and Rocksteady very rarely leave each other's side. If Rocksteady didn't have his gigantic crush on April there would be a lot more Ho Yay going on from the fans' point of view.
Baxter Stockman and his gender-neutral (but still male-sounding) alien computer, Zee. Watch an episode with them in it and see for yourself.
Sometimes happens to the turtles themselves.
Hollywood Pudgy: From time to time, Irma will mention being on a diet, and although her size is mostly obscured by a baggy turtleneck sweater, on the few occasions she wears something else, it's clear that she certainly isn't even fat at all.
The episode "Zach And The Alien Invaders" is easily the biggest offender of this in the entire series, considering that the whole premise is about Zach convincing the turtles that he's seen aliens, and robots, and other dangerous things that ended up being harmless, and getting in trouble for it. Because it's not like the turtles have ever fought aliens or robots before, except you know like every episode where Krang and Shredder attack the turtles with the Foot Soldier robots which happens on a regular basis! Later on Zach does see aliens that are trying to take over the world, and helps the turtles stop them, but the episode basically sends the message that "it's OK not to listen to kids". To be fair the episode was trying to go for a "Boy Who Cried Wolf" type of Aesop, but didn't pull it off very well.
The episode "Leonardo Is Missing" also falls under this, which is lampshaded by Splinter at the end, but unlike the first example, this episode is actually still fun to watch.
Splinter: Next time you leave Leonardo, make sure to leave a note.
Any time Shredder and Krang rely on Bebop and Rocksteady for a plan but special mention goes to "Super Rocksteady and Mighty Bebop" when a plan to mind control New York failed because Bebop and Rocksteady's first attempt to install the machine damaged it causing it to malfunction. When Krang notices it's not working right his response, is to send them up to fix, rather than go himself or send Foot Soldiers, or anything else not effected by the machine. After he asks them how many more times they intend to fail, they state they will do so lots more.
Baxter Stockman. Starting out he was just trying to legally make money off his inventions and the Shredder offered him work, but then tried to murder him to keep him from saying anything about his plans, and after being rescued by the turtles his left died to telephone pull. In Season 2 he's shanghaied by Shredder into helping him again and the abuse he takes eventually turns him into a full blown villain and he's turned a mutant fly. Later he tries to make himself human again and the turtles stop him for no good reason by kicking him into a dimensional portal where he's apparently eaten by a spider monster. He's one of the least evil villains on the show but the only one with a (heavily implied) canon death.
Shredder is a Jerkass who wants to Take Over the World, but he's working with a partner who was absolutely no respect for him (even one the rare moments when his successful), is constantly humiliated by the turtles and has his plans thwarted by the sheer stupidity of his two minions.
Les Yay: Some fans see this with April and Irma, some even like to insist that Irma wants more than just friendship from April; and Irma always clinging to, or sometimes being protective of April kind of eggs this on.
Shredder crosses this in the first episode of season 8 when he actually destroys the Channel 6 building which takes it out of commission for the rest of the series.
In the same episode, it is stated by Bezerko that Krang committed genocide against his people, because he had no further use for them.
Long before that, there was Shredder intentionally exposing April to the lethal fumes of the Doku plant back in "Enter: The Fly," which very nearly killed her. And this was back in the second season, which had already been made Lighter and Softer than season 1!
Bebop and Rocksteady cross this in "Shredder Triumphant" when they try and shove the Channel 6 crew out of a window.
Krang likely crossed it sooner in "Return of the Technodrome" when he tries to destroy New York with an earthquake after its populace refuses to vacate the city so he can use it as a base of operations.
Narm: During the early seasons, they weren't in the territory of Family-Friendly Firearms yet (being in syndication instead of a network), but it seems that somewhere along the line communications got muddled, and as a result, you'd hear a line like "the bullets aren't stopping them", while the guns being fired are shooting lasers!
Seymour Gutz falling apart in a vat of mutagen in "Enter: Mutagen Man". It's Played for Laughs and he survives, but still.
The Mutagen Man action figure isn't any better- it's a small batch of connected organs and a skull floating inside a clear container with limbs grafted on that are covered in torn flesh and exposed bones. Yes, this was sold to kids.
Older Than They Think: When most people think of a morally ambiguous ninja girl with a tempestuous and sometimes romantic relationship with Leonardo, Karai always comes to mind and not Lotus Blossom from this show. Lotus, in fact, predates Karai, having been introduced in 1989 whereas Karai only came about in 1992.
Replacement Scrappy: Dregg wasn't really a bad villain by his own terms, but the mere fact that he wasn't Shredder ensured he never became popular. It didn't help that Shredder had become genuinely threatening again during his last season before being replaced by Dregg. Not even being voiced by Tony Jay could save Dregg from the Scrappy Heap.
Carter, considering he sort of replaced April in season nine (though she would take the role back in season ten).
Rooting for the Empire: As Shredder, Krang, Bebop and Rocksteady have what many fans agree as the funniest scenes in the show it can hard not to root for them. Shredder in particular since he never catches a break even when he wins.
Rescued from the Scrappy Heap: However, Zach did have his share of valuable moments like when he saved April's life in "Bebop And Rocksteady Conquer The Universe" and the turtles' lives in "Night Of The Rogues", which both earned him a good amount of fans.
Carter has a few fans, but most of them agree that he doesn't really belong on a show like TMNT.
Burne and Vernon aren't well liked either. Especially for being huge selfish jerks and constantly bad mouthing the turtles, even when they saved their lives.
Though they were intended as ineffectual antagonists, so it would be more weird if people actively liked them. Considering they're both chew toys as well, Vernon especially, it's more of a case of Intended Audience Reaction.
Most Filler Villains, due to being unoriginal (almost all of them are gangsters or mad scientists, and nearly identical ones at that), and the fact that they just aren't as interesting as Shredder or Krang.
Seasonal Rot: Some fans agree that this happened during Season Eight, when the sky was permanently red and the show took on a Darker and Edgier tone.
Having said that, Season Eight isn't entirely without its fans; a few consider it to have struck a good balance between the show's original tone and that of the comic book. In addition, Shredder became a serious threat again for the first time since the very beginning of the show. However, fewer people are willing to defend Seasons Nine and Ten, when Lord Dregg replaced Shredder and Krang. Though the 3-part "Return of Shredder and Krang" arc in the middle of season 10 does have its fans, with many feeling that it served as a better finale to the show than the actual series finale.
Season Two is widely considered this: not as good as the short first season preceding it or the long third season following it, but perfectly watchable regardless. The "Eye of Sarnath" Story Arc and "Enter The Fly' are considered its highlights.
How a lot of fans feel about Season Five. It has some of the series' best ("My Brother, the Bad Guy") but it also has some of the series' worst ("Donatello's Badd Time" and "Zack and the Alien Invaders")
Those goddamn pizza toppings. This may be why the Red Sky seasons did away with them completely.
Baxter's mutation into a fly.
The turtles' mutation in season 9.
The sewers. Lampshaded constantly.
Tear Jerker: Though much more lighthearted than the 2003 version this show still has its moments of this. One of the most memorable is the episode "Turtles, Turtles Everywhere." Shredder and Krang reprogram a network of robotic garbage trucks and order them to capture "the turtles." With no knowledge of the TMNT, the trucks start rounding up every turtle in the city, and eventually what is said to be the last surviving member of an endangered sea turtle species, just as she was about to lay her eggs. One of the reasons it's such a great episode is that, unique among shows in The '80s, it's actually a Green Aesopdone right. Unlike Captain Planet villains and much more similar to real-world polluters, Shredder and Krang aren't actually intending to damage the environment as its own end; they're just greedy and don't care if it's a side-effect. At the end of the episode, they put a stop to the plan and return the sea turtle to the beach to finish laying her eggs and the resident joker Michelangelo starts sobbing as she swims off saying that she reminds him of his mother. Also, while they attempt to end the episode on a humorous note after that bit, it actually becomes sadder when rewatching it as an adult, when you can think about it enough to worry that even though the sea turtle got to lay her eggs after all, based on April's claim that she was the last surviving member of her species, the eggs might not have been fertilized. So she could still be the last of her kind, ever.
In the episode "Splinter No More", it's pretty hard to see Splinter lamenting his loss of his humanity to the point of shedding tears. This becomes much Harsher in Hindsight when you remember that Splinter destroyed Shredder's Retro Mutagen Ray in order to save the turtles, but also destroying the one thing that could return him to his human form in the process.
Also in the episode "Hot Rodding Teenagers", it's tough to see Kala break down as she explains that the only reason that she and the other Neutrinos are on the run is because that they are kids who would like to have fun instead of fighting in Dimension X's infinite war, and are being hunted down for it.
Kala: "You don't know what it's like.... living in a place where everyone wants to do you in....just for the crime of being young." (She starts to cry.)
The beginning of "Splinter Vanishes".
The penultimate example for most fans of the original series is in the opening episode "Get Shredder" where Shredder actually destroys the Channel 6 building which takes it out of commission for the rest of the series.
Michaelangelo has his moment of this when he thinks everyone forgot his birthday in "Michaelangelo's Birthday", which makes it even worse when he runs into Shredder.
Splinter in "Splinter No More".
Donatello in "Donatello's Duplicate" easily counts for this.
Leonardo in "Take Me To Your Leader". Even this Leonardo-neutral fangirl wanted to hug him.
Raphael in the beginning of "Raphael: Turtle Of A Thousand Faces".
Baxter Stockman, even when he was a Jerk Ass. Some scenes where he's abused and mistreated are actually pretty uncomfortable to watch.
Krang sort of was one in "Hot-Rodding Teenagers from Dimension X". It's the sadness in his voice when he tells General Traag how he lost his body when they "banished him to this miserable mud-ball" as well as how upset he was about Traag and Granitor seeing him without his body.
"Night Of The Living Rogues". Fed up with Bebop and Rocksteady's incompetence, Shredder gathers a large group of the Turtle's previous enemies to defeat them once and for all. The Turtles are completely helpless against the assembled baddies. So will this cause the the Turtles to call on all of their allies, like The Mutant Frogs, Usagi, Mondo Gecko and Mona Lisa leading to a huge brawl between the groups? Nnnnnope. Instead, the Turtles just call on Casey Jones and Zach the "fifth turtle" for back up, and the villains run away at the end when it's pointed out that they're outnumbered. Keep in mind that one of those people is a kid, and the other two are April and Irma.
The subplot of "Krangenstein Lives!!" Shredder loses his memory. Pretty interesting right? You'd think they'd go for something different but... he's still evil, he just can't remember his name. There are so many different ways that could have gone.
The seventh season had an episode called "Dirk Savage: Mutant Hunter", where an eccentric billionaire who is secretly a mutant slug plotting to take over the city named A. J. Howard hires bounty hunter Dirk Savage to capture all the mutants in New York. Considering the episode's focus on mutants and the large number of mutants the show had, you'd expect fan favorites like Mona Lisa or Muckman to return, but this was not the case. While Mondo Gecko and the Punk Frogs Napoleon Bonafrog and Genghis Frog returned in this episode, the only other mutants that appear in the episode are Tokka and Rahzar from the second movie and a bunch of unnamed mutants created solely for this episode. It's still a good episode, just an example of how good things could have been better.
Fans who dislike Bebop and Rocksteady often wish Baxter stayed The Dragon to Shredder in Season Two.
"Attack of The 50-Foot Irma!": The "Giant Shredder" plotline is dropped near-instantly despite how cool it would have been for the Turtles to fight him.
Villain Decay: Shredder and his cohorts. A case of Tropes Are Not Bad, as they became a lot more funny and unique. And reversed in the "Red Sky" seasons which saw Shredder become much more competent and dangerous.