These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
One caused by dub changes. When he smiled and shook his head, did Jiŕnliáng/Henry forgive his father for causing the Tamers' digimon to need to return to the Digital world or not?
In the original Japanese, Zhčnyǔ admits to his son that what he did was unforgivable, and looks down in shame. In the English dub, Zhčnyǔ just tells his son that things will get better.
Is ADR-01 (AKA J-Reaper) like the rest of the D-Reaper's agents, a mere puppet following the singular will of the program's directive of observe and destroy, or has it achieved some degree of independent sentience? Or is it perhaps somewhere inbetween?
Ass Pull: While the method for defeating the D-Reaper can come off as this since the show seemed more interested in building up how invincible it was than finding a way to defeat it, nothing compares with the Cruel Twist Ending where it turns out the Digimon can't remain in the real world, something that was never forshadowed earlier in the series.
Guilmon growing a phantom version of Megidramon's tail to smack away Beelzemon's bullets.
Vajiramon and Pajiramon eating electronics to stabilize themselves on Earth, something which no other Digimon ever showed the need to do.
Broken Base: There are two kinds of Digimon fans. The fans that love this season the best for being Darker and Edgier than Digimon Adventure and Zero Two and fans that hated this series for taking place in another universe and completely dropping the characters they have come to love over the course of two years.
Whether Runaway Locomon and/or Message in a Packet are canon.
Canon Sue: Ryo falls into this at times. The Ace who spontaneously appears in the middle of the Digital World (and the plot), who is skilled enough to train the ferocious Ultimate-level Cyberdramon and carries some of the most powerful cards in the game (a lot of his battles are actually won by the use of these cards rather than actual skill, which doesn't help his case), who is worshiped for his celebrity status, and who somehow achieves a Biomerge Mega form (that he can use in the Real World) off-screen. A lot of fans only barely tolerate him for taking some of the pressure off of the main trio and for his sexual tension with Rika.
Fanon: Ai and Makoto are not twins (Ai is clearly older than Makoto), but good luck finding a different reference to them.
Fanon Discontinuity: As mentioned elsewhere, the CD drama which retconned the second movie. The fans, however, gleefully ignore it, or try to connect them anyway.
Growing the Beard: If the first episode didn't at least show some impressive stubble for a Digimon anime, then the appearance of the Devas should have been when the full beard grew out... and then Beelzemon's appearance should have been when the beard hit the floor.
Harsher in Hindsight: In-universe example. Takato used to cry a lot in the first episodes because he was really afraid of losing Guilmon. Cue the last episode.
He Really Can Act: Steve Blum, who is Yamaki, Guilmon, and Kenta here. At the time it was widely believed that the Yamaki voice - his standard, also heard in The Big O as Roger Smith - was all he could do. Add a little growl, you get his Wolverine. Add a little more growl, you get BlackWarGreymon. But then he does Standard Blum Guy (Yamaki), the dorky Kenta, and the very unique childlike-but-low-pitched voice of Guilmon and makes none of them sound anything alike, to the point that admit it - you had no idea he did all three before you read it.
Televisions and computers use the same Chromatic Arrangement. In 2010, Sharp added yellow into that protocol as a fourth color when they rolled out their Aquos Quattron LCD TV.
Juri chased Leomon around the park insanely, claiming that it's their destiny to become partners, much to Leomon's horror and confusion. Watch as they do become partners, and Leomon does a complete 180 on his view of her.
It is not uncommon to hear Adventure fans to blame the change in universe and the darker tone contributed for Digimon's decline in the West.
It had unfortunate timing - 2001 was pretty much the peak of the Mons fad.
Fox Kids, the program block that Digimon appeared on, was also being cancelled at the same time, leaving Digimon to appear on a different channel, at inconvenient times, which was also something that was already in motion before the Digimon Tamers dub even premiered.
Tamers is blamed for the start of other Digimon series taking place in universes outside of Adventure. However, that is actually Digimon Adventure 02's fault.
Values Dissonance: Rika/Ruki openly embracing more of her "feminine" side is seen as a sign of maturity to Japanese viewers. Westerners are not so open to the idea of stereotypical femininity and gender roles. The dub didn't really make this any better when they made her seem like she disliked wearing dresses (when supplemental images from Japan stated the opposite) which made it more confusing when she becomes "feminine" in the end.
Vindicated by History: When it first aired, many fans of the Adventure series were disappointed and confused by the lack of relation between the stories, and much of the theming and subtext was lost on younger viewers. Over a decade later, thanks to both access to the Japanese version and a higher demand for more cerebral, deconstructive series, Tamers has gained a large amount of popularity, and is easily the second most popular Digimon series on both sides of the Pacific.
What Do You Mean, It's for Kids?: Very much of the "was this content really created with children in mind?" variety. Head writer Chiaki J Konaka, frustrated by the lack of gravity death is typically treated with by children's media, made it a point in Digimon Tamers for death to be permanent and traumatic. Which some people found rather troubling.
And, hell, one of the whole reasons for the Broken Base was due to feelings that the Moral Guardians might be in the right - showing the show to the later-elementary-age kids who are the (nominal) primary target of the show is a crapshoot as to whether they'll "get" it. Showing it to the kindergartenders on the young end of the target demo usually ends in tears and nightmares and is not recommended.
Of course, on the other end of the spectrum, these same elements made it and continue to make it vastly, vastly more popular with nearly every over-school-age periphery demographic.
The very first episode. A Malidramon lunges at the jugular of a DarkTyrannomon, which explodes as it evolves into MetalTyrannomon, which then squashes the Malidramon with its palm.