Abandon Shipping: Some fans end up losing interest in Tomoyo x Sakura the moment it's revealed that they're actually second cousins. Unfortunately, CLAMP fans who find incest uncomfortable may have to navigate past a lot of it.
Alas, Poor Scrappy: Even many who hated Meiling felt sorry for her getting her heart broken by Syaoran.
Badass Decay: Syaoran is a justified, plot enforced example. While he remains a Badass Adorable all throughout the series, in earlier points he could take on threats near single handed and in the anime could collect and skilfully use the Clow Cards himself. After the finale judgement, the cards are solely Sakura's property, thus he loses that power boost, and most threats are tests designed specifically for them to be used on, meaning Syaoran's usage is mostly limited to protecting Sakura as she carries it through. His personality also becomes blatantly less badass as the story progresses (though to many that's a good thing).
During the segments where Sakura tries to identify the Clow card of the week and their current movement, Kero and Sakura used the cards for fortune telling and determined that 'The Mirror' card is targeting Touya. The fortune telling abillity is never foreshadowed, never used by anyone else (Not even Clow himself) and is never mentioned again. Though that's only in the anime; the manga mentions it early on in regards to the Fly card.
NISAmerica's decision to add the Animax dub in their DVDs. Some are happy it's uncut and uncensored and that the voices actually match the characters better, even if the voice acting is a bit shaky, while others claim it to be even worse than the Nelvana dub and wish the latter was included instead. Others wished that it was completely redubbed.
The Teacher/Student Romance between an adult man and a fourth grade girl is seen as either adorable or the single most disgusting thing in all of manga. There is no middle ground on this one.
Cut-and-Paste Translation: Nelvana, with "Cardcaptors", was responsible for much of the cast getting a Dub Name Change and removed all romantic subplots of any kind (not all convincingly). The US broadcast on Kids' WB! attempted to widen the show's appeal beyond its original demographic by switching the focus from strictly Sakura's point of view and pushing the idea of Sakura and supporting character Li Syaoran being more like partners by rearranging and splicing episodes and tweaking scripts. This would have actually been convenient in later episodes, which play a lot more from Syaoran's perspective and give him a rather prominent partnership with Sakura, unfortunately the unwanted romantic context of most of this footage actually led them to take out a lot of the character's relevance. And even with all the butchering they did, they couldn't remove the subtexts. It's still pretty obvious how Syaoran and Sakura feel about each other.
It also was wildly popular in Mexico, thanks to a really good dub, compared with the English one. It does help that Cloverway managed to get the rights of the original Japanese version from NHK, rather than getting the same rights from Nelvana, despite Nelvana having rights for the whole American continent besides the U.S. and Canada. In fact, the series was widely popular in the whole of Latin America, in part thanks to the Mexican dub and because it was aired at prime time by Cartoon Network in the region, and amongst other anime such as Saint Seiya, Maya the Bee, and Dragon Ball, it found a place in the pop culture, becoming a staple of the 90's generation childhood memories.
Girl Show Ghetto: For the most part its averted thanks to its engaging characters (and the fact that Tomoyo designs costumes just so she can throw Sakura into them), interesting story, and some dark undertones, though some haters may accuse it of falling into this somewhat due to its normally bright and idealistic nature and in-universe romance...pretty much why Cardcaptors, the edited dub, exists.
Growing the Beard: For many the second and third season are held with greater interest. While the first season was enjoyable, it was a fairly formulaic Gotta Catch 'Em All series. Starting from Season Two, Character Development kicks in, key characters like Yue and Eriol enter the scene and a greater sense of continuity occurs. And of course, Sakura and Syaoran's romantic arc begins...
Toya tells Sakura that she isn't fit to be a princess, then Tsubasa Reservoir Chronicle came out with Princess Sakura as a main character.
Numerous fanfics had Sakura as a princess with Syaoran as a prince or someone who loves her, and equally vice versa. Come Tsubasa, and that's what happens.
The Sealed Card movie has Sakura playing a princess in a school play and brings in the point of sacrificing one's love to capture Card #53. It doesn't happen, but then, what happens in Tsubasa? More recycling.
Avalon Code has several resemblances to this, which makes Sakura's dub surname Avalon an amusing coincidence.
When Sakura's father speaks to her class about his job, Syaoran shows quite a bit of intrest in archaeology. Come Tsubasa, that version of Syaoran is an Adventurer Archaeologist.
Nelvana and Kids' WB!'s attempts to boost Syaoran as a co-lead in the Cardcaptors dub come off as ironic following his gradual evolution as Breakout Character for the original anime (and CLAMP media as a whole). Even more ironic since it was through a romantic arc, which Nelvana had attempted to omit all traces of.
Sonomi had a crush on Nadeshiko, but it was one-sided.
The Light and Dark cards.
Macekre: The English adaptation known as Cardcaptors was edited and modified in an attempt to downplay the cutesy shoujo factor and moderate it for easier audience consumption across the board. In addition to also being a shoddy attempt at doing so, it was not looked upon favorably by the original fans or many new ones; production and DVDs for the series stopped being made after it was noted the original version released at the same time sold much better.
Misblamed: 4Kids Entertainment often takes heat for Cardcaptors from people who don't know all of the facts. Nelvana itself gets unfairly maligned for the "Syaoran as main character", which was mostly caused by Kids' WB! leaving out several episodes (the first episode aired is Syaoran's debut, the eighth episode) and promotions playing up Syaoran's role much more.
Sakura starts off as a small example, but by the end of the series she is probably a Trope Codifier. Hell, Sakura even won the first ever Saimoe Tournament. (The TV show certainly marks the point at which the anime production companies noticed the Peripheral Demographic that sprang up around characters like her, and their buying power.) This is toned down slightly in the Nelvana dub, where she is given a more 'tomboyish' attitude and some of her 'cuter' or more vulnerable aspects are edited out.
Tomoyo also counts to a slightly smaller extent; she also made it to the semi-finals (Top 4) of that very same tournament.
Moral Event Horizon: The Enchantress' practicing dark magic, despite Clow's warnings. It went as well as expected.
Sakura's gleeful calls for "Syaoran-kun" following the same pivot. Granted since she was close to him a good while beforehand, she milks it a lot more.
Narm: When Syaoran, upon being confused on who he truly likes, Yukito or Sakura stumbles into the latter. In the manga, they had gone into First Name Basis earlier thus she calls him Syaoran-kun making her joy seemed genuine as is he is one of her closest friends. But in the anime she calls him Li-kun as they are still on a Last Name Basis since this is before they get trapped in an elevator. This makes this moment less impactful as being called by last name is the equivalent of being more formal towards each other like an ordinary friend instead of someone special.
Never Live It Down: According to fandom, all Kaho does is seduce her students. This is based on her relationships with Touya, a former student from her time as a student teacher, and Eriol, the reincarnation of a centuries-old sorcerer who only looks like a child so he could blend in with Sakura's class and never was Kaho's student.
Periphery Demographic: Owing in part to the hilarious, cutesy and heartwarming nature of the series (and probably because of quite a bit the Yay subtext too), this show has a surprisingly large viewership of boys, older teens and even middle aged adults, clearly evident from the statistics of any popular video on the internet.
Romantic Plot Tumor: In the last part of the series a lot of time is spent on Syaoran's mounting feelings for Sakura, to the point where quite a few fans thought it started impinging upon the rest of the plot. This affected the English dub (which edited out most romantic elements) to the point that a lot of later episodes, came out empty and non sensical when diluted to the remainder of the plot, often retooled into clip shows.
Die for Our Ship: In the fandom just about everyone has been targeted by Shippers at some point or another for being in the way of their OTP. Syaoran, Nakuru, Kaho and Mei-Ling are the preferred victims. There's enough to warrant its own page, and that's not even complete.
Spoiled by the Format: You can almost always tell when Sakura is going to miss the catch, simply because her attempt is actually animated instead of stock footage.
Squick: Some can see some of the relationships, based on Incest Subtext and Teacher/Student Romance, as this. For others it's not the relationships themselves but the rather sugary way they're treated that falls into this trope.
Sugar Bowl: It isn't a world so straw as to bash anyone for not being a part of their happy land (mainly because the series doesn't even have a real bad guy), but CLAMP purposely made Card Captor Sakura a place where there is acceptance of all minorities, sexual orientations, children, adults, boys, girls... to set a good example for the children growing up watching it. You'll notice that there are no malicious adults in this series. At all. The few adult characters that start out looking like they might spoil for a fight (for example, Sonomi's aggression towards Fujitaka) are quickly resolved and they join the Big Happy Family).
They Wasted a Perfectly Good Character: All the cards have a sentient form that has to be defeated when they are captured. For the large part after a card is captured, they are utilised solely as powers for Sakura to use, their physical forms seen only on their card's picture afterwards. Only a handful such as Mirror and Dash make a sparse reappearance.
Values Dissonance: This series has an astonishingly casual view of May/December teacher/student relationships. Sakura's mother and father met when he was a high school teacher and she was his student. Sakura's older brother and his (student) teacher had a brief romance, but dropped it for reasons that had nothing to do with age inappropriateness. One of Sakura's prepubescent classmates has a crush on their teacher... and he returns it! And this is shown as romantic and dreamy. One can hardly blame Nelvana in this instance: they changed a line about Rika loving her teacher to Rika fearing her teacher.
Vocal Dissonance: Nelvana dub decides to give Kero, a cute and tiny little critter, the voice of a 20-something year old man with a surfer tone. The Latin-American and Portuguese dubs are guilty of this too, even though they're known for Superlative Dubbing. Thankfully, the Sealed Card movie and the Catalan dub give him suitable voices for both his plushy and beast forms.
The Woobie: Being a CLAMP work, the large majority of characters have at least some vague tragic aspect to their personality.
Sakura may be the most consistent example throughout the series' run, due to her occasional Moe aspects and more fragile emotional disposition, as well as being unwillingly dragged into the role of Cardcaptor to begin with.
Yukito is one during the Sakura Card arc. Yue is also revealed as one after a flashback shows how much Clow's death hurt him.
Also Meiling in Episode 60. In general, her bratty attitude stems from a massive Inferiority Superiority Complex, especially seen in how much effort she puts into living up to her boasts about being good at everything.