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.
YMMV: New 52
Author's Saving Throw: Martian Manhunter told off his Stormwatch teammates for referring to him as a Justice League member, which is apparently shorthand for "established superhero", despite the fact that the Justice League has never had more than seven members (until JLI). So, any author wants to refer to, say, Metamorpho or Green Arrow as "Justice League heroes", that's what it refers to.
Broken Base/Internet Backdraft: The reboot in general was very controversial when it was announced, and even two years after it happened opinion was divided and discussions could get very heated about certain aspects of it. Overall, some fans consider it an interesting and fresh new take on the universe, while others consider it the return of some of the worst tropes from The Dark Age of Comic Books.
Superman is introduced as a more angry brooding figure considerably more violent than any previous incarnation being willing to throw defenseless white collar criminals out of windows and dangle them off ledges, mocking the police in his early twenties and choke slamming Batman in their first encounter.
And of course, the Executive Meddling is still going strong. Some fans are upset that the comics appear to be even more editorial driven than before the reboot.
The disappearance of long time fan favorites such as Wally West (the third Flash - along with his wife and kids), Cassandra Cain (Batgirl II/Black Bat), and Stephanie Brown (Spoiler/Robin/Batgirl III/etc.) among others while supposedly "inferior" or less beloved characters such as Bart Allen remain has not sat well with many fans.
It's the Same, Now It Sucks: A common gripe with the New 52 is that despite a large number of changes, the Continuity Lock-Out that was typical for the old DCU did not disappear, and many characters (such as Green Lanterns) still require extensive knowledge of their old DCU stories to understand what is going on, instead of having a fresh start. What makes things even more confusing is that many older fans who would be otherwise immune to Continuity Lockout are confused as well, due to the fact that whatever continuity that has been retained has been very hazily defined. For example, according to the new "superheroes debuted five years ago" compressed timeline, Batman started his career and took on all four male Robins within six years.
Tainted By The First Issue: Since DC released fifty-two first issues in one month, even people willing to buy all fifty-two #1s were unlikely to give anything they didn't like a second chance. (How many #2s are you going to buy of comics you already have a bad impression of? When there might be dozens of them?) Ergo, any writer who put something controversial in the first issue, expecting readers to stick around for justification in later issues, was making a grave mistake. Several of the series died due to their first issue not being as good as later ones.
However, the "add something controversial to hook in fans" thing was a double edged sword. Catwoman and Red Hood and the Outlaws drew in massive amounts of outcry and drama over scenes of sexualization (Catwoman having rough sex with a hesitant Batman, Starfire in some cheesecake poses and having sex with Roy Harper with the then percieved notion that she couldn't tell humans apart). How the writers responded to the allegations of angered fans differed: Judd Winick didn't really do much to defend himself and was replaced rather quickly, while Scott Lobdell openly responded to fans and lasted much longer on his book.
Superman was reintroduced as a man who in his early twenties was violent towards non powered criminals, openly mocking the police as he ran from them and a few years later in the timeline, choke slams Batman in a fight when he already knew nothing in Batman's arsenal could hurt him. Even the more grown up version introduced in issue one of a parallel series was shown to be a more angry brooding figure than Superman had ever been.
One of the reasons for this reaction was that quite a few titles suffered from an Aborted Arc in their cancellations - although most of them wrapped up fairly smoothly, there was still a small forest of dangling plot threads left behind, presumably now never to be resolved.
One of the most controversial examples of this in fandom is giving The Phantom Stranger a definitive origin.