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.
Complete Monster: Stanley Dover Sr. was the secretmain villain of the Quiver arc. We first meet Stanley Sr. when Green Arrow rescues him from a mugger. Stanley Sr. comes off as a kindly old man and even becomes Green Arrow's assistant. However Stanley Sr. has a secret, he has been a Satanist since the 1950s. His wife left him when he suggested they sacrifice their first born infant to a demon to gain immortality. No longer married, Stanley Sr. traveled the world and studied the occult. Decades later he returned to America and moved to Star City. His daughter Shelia now grown up, made contact with him. Wanting to remain respected by the community, Stanley Sr. pretended to be a loving father. Shelia would often have Stanley Sr. baby sit her infant son, Stanley Dover Jr. One day, while baby sitting Stanley Jr., Stanley Sr. attempted to summon the Beast With No Name and bind it to him. However the Beast bonded with Stanley Jr. instead. Years later, when Stanley Jr. was a teenager, Stanley Sr. found that the Beast had bonded to his grandson. So Stanley Sr. kidnapped his grandson and began to torture and starve him to force the Beast out. Stanley Sr. began to murder children and feed their blood to his grandson. Stanley Sr. eventually revealed his true colors to Green Arrow, planning on transferring his soul into Green Arrow's body to further his power mad quest. Stanley Sr. also plans to rape Mia Dearden, a former teenage prostitute Green Arrow had recently rescued.
Contested Sequel: Andrew Kreisberg and Ben Sokolowski's Green Arrow run, from before it started, was already drawing ire for replacing Jeff Lemire's run on the book, thanks to Lemire saving the series from the slum it was stuck in following the reboot. This isn't helped by the fact that the two are the ones behind Arrow, which has a Love It or Hate It response from the comic book fanbase, making it appear they'd morph the book into essentially being a reiteration of what they're doing on the show (a criticism not exactly unfounded, given the inclusion of Felicity Smoak, as well as reintroducing Merlyn, and dropping most of the previous supporting cast save for Diggle (a character originally introduced on the show), essentially leaving the same Power Trio featured on the show), something that even fans of the show are mixed on. However, they do also reintroduce Mia Dearden, a character who's been missing since the reboot, and bring Oliver back to his mouthy left-wing 'man of the people' characterization that he's been missing for a while, making it more like the classic Green Arrow status quo.
Die for Our Ship: There's a surprisingly large number of Black Canary fans who hate Oliver and want to see him killed off, allowing her to hook up with various members of the Birds of Prey - usually Oracle.
Growing the Beard: Quite literally; the new characterization that came with the beard made Ollie a standout character.
Ollie's new series in The New 52 reduces the beard to a stubble. And the series hasn't been overly well received.
For the New 52 series, Jeff Lemire taking over the title with issue #17, removing some of the unpopular elements from the previous run.
Connor had even more chemistry with Ollie's ex-CIA hate-friend Eddie Fyers, with whom he traveled and lived with for nearly the entirety of his run. Fans seem to gloss over this one, although there's probably a reason for that...
There's also a few Oliver Queen/Hal Jordan fanfics (and wisecracks in the regular comics now) that give new meaning to the term "Hard-Traveling Heroes".
A meta-example could be Ollie and Identity Crisis writer Brad Meltzer who has admitted he has a man crush on Green Arrow.
There is also Roy Harper and Nightwing (Dick Grayson).
Never Live It Down: Roy Harper's two-issue struggle with drug addiction has pretty much defined the character ever since.
Also, the Shado rape incident, which was treated as though Ollie had cheated on Dinah.
While he never got married, many fans believe Connor Hawke's few romantic relationships were forced as well, due to the fears of certain writers that the asexual monk might be viewed as being gay. And we can't have that, can we?