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.
Regarding Devin Grayson, one of the main writers of his long run. She's either the cause of several majorly terrible story arcs and a massive Dork Age, a decent writer who just wasn't writing at her best at the time, or a great writer whose run was unfortunately hijacked by Infinite Crisis, which prevented her from finishing off the story.
The New 52 red suit. Brett Booth reintroducing the fingerstripes (and adding hip and neck stripes) has been universally accepted as a welcome olive branch, but you fall into one of two categories here: either you think red/black is a dark, edgy look and appreciate the fact that most of the Batman characters now match, or you think the idea of Nightwing needing to be dark and edgy or match the other Batman characters is ridiculous.
The announcement of the Grayson series lead to a big one regarding the premise, which is that Dick would become a secret agent, something he'd keep from Barbara and Alfred. Some like the idea, thinking it's a nice idea (although even they hope it's temporary), and others think it's a stupid idea that doesn't suit the character or his history, or simply that it simply doesn't make any sense, since Dick's one of the most famous people on the planet since the Crime Syndicate unmasked him in Forever Evil.
The most polarizing aspect being that Dick uses a gun now. While he had a gun for a longtime thanks to his time as a cop in Bludhaven, he never actually used it and said he never would.
Ensemble Darkhorse: DC Comics' official position is that he's the most beloved superhero in the community (yes, even moreso than Superman) and that almost any member of it would instantly drop what they were doing to help if he were in trouble.
He seems to have a slight amount of this in real life as well. The producers of Arrow have said he is their "holy grail" of characters they'd like to appear on the show if they can, and he seems to have a permanent spot on the list of DC characters fans hope will eventually be realized in a live-action TV series or film, alongside others such as Wonder Woman or Zatanna.
Estrogen Brigade: He has the single biggest out of any comic book character, bar none.
Memetic Sex God: In-universe, every straight woman comments on how attractive he is, and the fandom loves to mention his nice ass and the finger stripes. In 2013, he was voted as the most dateable of DC's superheroes. He is very much the Memetic Sex God of the DC universe.
My Real Daddy: Bob Kane is credited with creating Dick Grayson, with some credit also going to Bill Finger... but Nightwing was created by Marv Wolfman, who had exclusive rights to the character throughout his entire run on New Teen Titans. Chuck Dixon is then credited with developing Dick's solo career in the 1996 Nightwing title.
Acknowledged by adaptations. Whenever Batman and Robin appear in an adaptation, the credits include a line to the tune of "Batman created by Bob Kane." Robin doesn't get his own credit. Nightwing, however, if he appears, will get his own "Nightwing created by Marv Wolfman and George Perez" credit.
Replacement Scrappy: Utterly averted when Dick became Batman. Fans were happy with the development he received and his partnership with Damian, to the point that many were disappointed when it was announced that he would return to being Nightwing with the New 52.
The Scrappy: While she's acquired a bit of a cult fanbase in the years since who attribute her flaws to the overall shoddy quality of the OYL arc, Cheyenne Freemont was very hated when she debuted in Bruce Jones' arc. It mostly had to do with her being abruptly introduced, coming off incredibly flat, suddenly being revealed to be a metahuman (making her come off as a Mary Sue to some), and other fans feeling that she was made to spite those who shipped Dick with either Barbara or Kory. Cheyenne was swiftly Put on a Bus by the end of the arc.
The Woobie: Not on par with Jason, but still very much a Woobie. He lost his parents at a young age, and his Parental Substitute doesn't respect him (or so he thinks).
As of the New 52, the guy can't catch a break. He inherited Haley's Circus, but it's destroyed by his Evil Former Friend Raymond for the stupidest of reasons. Then, after he's getting it rebuilt, The Joker then decides to blow it up and poison everyone, the result being a lot of people hating Dick, and him not being able to rebuild it because he put all his money into it. Then, he finds out Tony Zucco, the man who had his parents killed, is still alive. His attempts to track him down, however, just result in a psychopath getting wind of incriminating info on the mayor of Chicago (where Dick has moved to find Zucco), which is promptly used to motivate said psycho into taking over Chicago and causing tons of death, all of which Dick blames himself for. Then Forever Evil happened...