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.
Awesome Art: Rocafort's run as penciller for the book, his backgrounds were breath-taking.
Base Breaker: All three main characters have broken the fandom. Some don't like Roy has had years of character development and maturity (from being a father) stripped away to in order to make him Jason's sidekick. Some have criticized that Starfire has been written as a sex fiend without any of the character depth of her old incarnation. And some see Red Hood as just another generic "bad boy" anti-hero, and preferred him as a recurring Batman villain.
Designated Hero: Let's face it, these guys are not heroic in any shape or form.
They're getting better as the book continues though.
Fanon Discontinuity: The issue 0 revealing that the Joker basically orchestrated Jason's becoming Robin and his death (as in even Jason finding his mom). Suffice to say, many don't like it, since the Joker comes off as a Villain Sue, and out of character, and outright ignore it.
To be fair Starfire has always been like that, if anything, she looks weirder on Perez' original designs.
Growing the Beard: The first issue was highly controversial and caused many fans to judge the series as unlikeable (Jason), shallow and sex obsessed (Starfire), amongst other terms. The book has since subverted many of these preconceptions, despite the fact that there are still some people who refuse to look past the first issue.
Issue 6, which recounts how Starfire and Jason met, is also considered pretty good.
As is Issue 18, which gives closure to Jason's issues with Bruce and mends their relationship.
Hilarious in Hindsight: In the old 52 there was an AU sometimes called the Kingdom-verse that occasionally crossed over with the then mainstream continuity. In the Kindom-verse we were introduced to an older version of Lian (Roy's daughter from the old continuity) who went by the alias Red Hood. Note: This was long before Roy and Jason interacted much if at all.
This could also count as Heartwarming In Hindsight as well. If Lian is ever born in this continuity it's entirely possible that Jason, who is now teamed up with her father, will be a prominent figure in her life and would actually give her a reason to take up the name.
Internet Backdraft: The reaction to Kori's new personality was... not received well, to say the least. The fact that Lobdell's response was to call the people criticizing his portrayal of Kori misogynistic and xenophobic didn't help things at all, nor did the fact that he focused on the people using slut-shaming language towards Kori while ignoring the people who made well thought out, rational criticisms of the book's portrayal of gender and sex.
The fact that the characters are pretty much new ones sharing names and some basic background with their pre N52 versions.
Narm: Starfire's new costume is so ridiculous to many people that she's impossible to take seriously, and her sexual dialog doesn't help a bit.
Especially bad when she's standing next to Red Hood or Arsenal or both at the same time. You end up seeing two men who are armored semi-realisticly then you see a woman dressed in “clothes" that you wouldn't even imagine a stripper wearing. It becomes hard to take any scene seriously for most people.
Never Live It Down: The infamous first issue turned many people off from the series and years later is still one of the first things to surface anytime this book is talked about, however many recognize that it got better over time.
One True Threesome: Part of what was the first wave of fanart for the series. After the title had ONLY been announced.
And after issue one, in which Starfire has sex with Roy, and Jason states he'd "been with" her. In what might be a conscious rejection of the trope (and/or a retcon), issue six reveals this to have been spending the entire night talking with her.
Tainted By The First Issue: Again, that first issue outraged a lot of potential fans. However, it's a compliment to Lobdell's execution of his later issues that even people who absolutely hate that issue generally agree his handle of the characters got better. This is especially notable when comparing this #1's controversy to Judd Winick's antics on Catwoman #1. Noticeably, Lobdell clearly tried to address complaints head on, while Winick lost his book in part to the fallout from #1.
The Woobie: Jason, on top of being killed and resurrected, had such an awful childhood that he considers his birth as the happiest day of his life.
According to his happiest memory, even after all that happened, he still considers his time as Robin the best time of his life.
Roy's a recovering alcoholic, and at one point notes that he only has two friends. His happiest memory is Killer Croc refusing to kill him when he was trying to commit suicide by Croc. That isn't even starting on his trust issues.
Unfortunate Implications: One of the biggest causes of Internet Backdraft was Kori's line in the first issue where she says that she doesn't remember anything about her time on earth, which many readers took to mean that she has the memory of a goldfish and made the idea that she could consent pretty dubious. Later on it's shown that she was faking it, but even that doesn't come across as mentally healthy. Add to that the fact that Roy thought she really was amnesiac at the time and still had sex with her and he doesn't come out looking good either.