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.
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.
Freudian Excuse: In one retcon, Oliver was shown to have suffered Parental Neglect as a child. As an adult he became a stereotypical bored rich man who spent most of his time avoiding responsibility. After losing all his money he lost the one thing that made him happy, and tried to compensate for it by gaining the love of the masses as a hero for the poor and downtrodden of society. When in reality, he just wants to be loved, but even when he has friends and a family, and he doesn't know how to genuinely hold on to them and gradually drives them away with his jerkass attitude. He doesn't care about social ills, he wants to play the hero so people will love him. He wants love, but he's not very good at returning it in healthy ways.
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?