Broken Base: Given the poisoned chalice with which it started (the all-time worst Spider-Man story i.e. One More Day), the writers of Brand New Day had a steep challenge to get away from its shadow. Some fans have grouped two factions — "Traditionalists who believe it's good return to single uncommitted Spider-Man and "Progressive Fans who loathe it for being the Status Quo brought by One More Day. Linkara, host of Atop the Fourth Wall, is a Progressive, and has stated that he will not buy any more Spider-Man comics until One More Day is followed up on and addressed (and if it is, he'll buy every issue he missed- that's over one hundred issues). And then there's the "Good Storytelling Fans" who are willing to ignore the whole "married vs single" thing if the story is good and are generally annoyed by two other sides' endless arguments, preferring to take the work on its own and not as a part of the character's overall history.
Creator's Pet: Carlie Cooper. Good Gods, when will it stop! Everyone, and everyone seems to think she is the perfect woman for Peter. Including MJ who does it via hoping that she'd be good for Peter. Especially if you look at her as a Composite Character taking bits of old love interests and using them instead of giving her a genuine identity. Not helping her case, she's also named after Carlie Quesada, Joe Quesada's daughter - effectively making her a canon Self-Insert Fic.
The Gauntlet gets this as a whole, but most notably The Shred storyline, where Curt Connors eats his son and permanently turns into Lizard. The following arc, Grim Hunt, didn't fare much better and is full of several characters getting senselessly killed such as Mattie Franklin and Kaine, although the latter's death was eventually undone.
In general, most fans simply couldn't get into Brand New Day because One More Day was such a bleakfest with Peter openly being told that he's trading the love of his life for essentially an Ironic Hell, that the faux-cheerfulness with which the story started felt creepy as does the stated "lighter and softer" approach.
Dork Age: The follow-up of One More Day was obviously doomed to be this for many fans. It did end up being a dork age to many. Inconsistencies due to multiple writers, forced and unlikable love interests and just a weird way of not addressing what was canon and not... until it did with One Moment in Time, which only made things worse. It wasn't until Big Time when Dan Slott emerged as the MVP and started his run that it shook out of this rut.
Norman crossed it againby making Harry join his superhero team for the purpose of killing him, so he might be seen as a tragic hero. Thereby making the general public more willing to let him do whatever he wants. Yes, he planned to kill his son for good PR.
Lampshaded with Lizard.
Lizard: I feel strange. What's that feeling? Spider-Man: It's called shame. You killed a child. Get used to it.
Nightmare Fuel: Spot, after finally realizing how powerful he is. There's a reason why the guy Spider-Man saved from him went crazy Spot can go anywhere, there are no doors or locks or guards he cannot pass through. If he's after you, there is no safe place he will come and get you whenever he wants. He might be watching you right now, without you even realizing it, he can come after your friends or family and there's nothing you can do about it.
Refuge in Audacity: A scene in New Ways To Die. Harry finding his father in the office, wearing his Goblin outfit (without the mask) and holding a mug? Heh, relatively normal. Said mug reading "World's greatest dad"? You gotta have balls.
The Scrappy: Lots of new characters - Michele and Vin Gonzalez, Dexter Bennet and Carlie Cooper have sizable hatedoms, among others. Menace wasn't very well received by fans, but improved eventually.
Ship-to-Ship Combat: Dan Slott, Joe Kelly and Mark Waid had different ideas over which girl — Carlie, Norah or Michele, respectively — should be Peter's girlfriend. Results were completely insane, especially when other writers started picking sides. Not to mention Brian Reed decided to throw his hat in and started pairing Spider-Man with Ms. Marvel.
Win BACK The Crowd: Big Time, a "refocus" of the series which undid many of the changes brought about by BND has actually successfully resulted in a massive and consistent sells jump for the Spider-Man comics, although there are still some fans who think Dan Slott's run isn't setting the world on fire.
What an Idiot!: At one point, Peter is ordered by his corrupt new boss to take unfairly unflattering pictures of the mayor candidate, who happens to be father of Harry Osborn's girlfriend. Peter agrees, because he owes Harry some cash. It doesn't occur to him that his millionaire friend probably wouldn't care if he knew to get that money, Peter had to betray the father of the woman he loves.