The 2015 incarnation got some criticism from fans for frequently making supervillains more conventionally heroic. Most of the alignment swaps were undone for this series.
Most of the world building in the main series, while well done, was mainly in the graphic novels and movies, and not as much in the series. This show has more world building within the series, and more easily accessible material in the "Get To Know" shorts.
The 2015 series question of how Superman is a grown adult, while Lois is a teenager is assessed in "#Super Who?". There it's revealed that Superman is only a few years older then most of the main cast, 18-20 at most.
Family-Unfriendly Aesop: Parodied on "#HateTriangle" with Jessica's faith in pacifism being mocked and ultimately useless in saving the day. Jessica tries her best to hold onto resolving her battle with Star Sapphire peacefully, preaches on about how violence is terrible, but the villainess decides that she'll come back worse than before, rendering Jessica's message about true love completely moot. Though the show seems to hint that this was intentional for comedic purposes.
With ThunderCats Roar, since both are cartoons coming out in 2019 and both are sort-of reboots featuring iconic characters. Fans of DCSHG are seen bashing Roar for being created by a group of rookie creators and being unfaithful to its source material. They generally think their cartoon is superior, because it's created by cartoon legend Lauren Faust and it actually does something creative with it's premise. Not to mention the vast differences in female character design between the two works.
And to a lesser extent the Shea Fontana written/produced content. Fans of the Faust reboot will typically find the preboot content to be lesser. That said, some people miss the older series and prefer the more heroic versions of Poison Ivy, the theme song, etc.
Magnificent Bastard: Catwoman's brilliant scheme in #FightAtTheMuseum made her this. Originally plotting a simple break-in crime, she takes advantage of Supergirl's ego and effortlessly plays her into a clever trap, which involves the hero destroying half the museum, accidentally breaking a safe holding Kryptonite for the villainess to use against her, robs the entire place of all the valuables she desired, and frames the heroine for everything. The only thing that prevented her from getting away with all her loot was her underestimating Supergirl using her brain for once, allowing the girl of steel to escape just in time to catch up to the cat-burglar.
Like the previous series, Wonder Woman is once again made the lead over Wonder Girl despite the latter being more suited for the role as the Fish out of Water main character among a cast of teenagers, not helped by the fact the series is very blatantly a reworked version of the Super Best Friends Forever shorts which did feature Wonder Girl with the exact same personality and even voice actress Wonder Woman has here.
Similarly, Hal Jordan and Barry Allen being agelifted instead of using their younger counterparts, Simon Baz and Wally West.
The agelifted effect has also seems to have spread to all but Batman and Commissioner Gordon. Superman is only a few years older than the high-school-er characters, and characters associated with him like Lois Lane and Lex Luthor are now teens.
Unintentionally Unsympathetic: The girls (sans Diana) in #ShockItToMe. They're shown laughing at the humiliation of their other classmates (even Garth, whom Karen is supposed to be friends with) while excusing it as an embarrassing moment and that everybody has them. As such, it's just a little bit hard to pity them later on when Livewire publicly humiliates them, since they themselves were laughing earlier and only seem to care when they were the ones being mocked.