Arc Fatigue: Post-Flashpoint, whatever caused the falling out between Ollie and Roy. It's alluded to numerous times, and talked about without adding any detail. And just when you think they'll elaborate... they don't. It finally was explained in Green Arrow (Rebirth), nearly six years after it was first alluded to!
Broken Base: While fans were happy about the Rebirth series finally addressing what happened between Ollie and Roy, some of those fans were also not happy that Roy's backstory was made oddly similar to Jason Todd's backstory; homeless before he tried to steal from Ollie. Likewise, they weren't happy that Roy was now raised on a Spokane Indian reservation instead of a Navajo reservation, as though the tribes are interchangeable. Even the most critically panned stories from the New 52 were at least consistent with mentioning that Roy was raised on a Navajo reservation. While you could argue that this change was made to keep Roy closer to Oliver's home of Seattle, as the Spokane reside in Washington while the Navajo live in the southwest, it still is a controversial change nonetheless. There were also those who disliked the retcon on why Roy left the reservation. Originally, his adopted father sent him to live with Ollie because he was dying of liver cancer, while here, Roy was framed for his adopted father's death and kicked out of the reservation because he was too drunk to remember if he did it or not. He didn't. Fans felt this added unnecessary drama to Roy's backstory and didn't like that he was now already an alcoholic before he met Ollie.
"Hunters Moon": Al Muncy/Muncie is the heir to a bootlegging fortune. A sadist with a penchant for children, Muncie stalked the streets of Seattle to kidnap multiple children, hold them captive and torture them for days on end until death. Only his last victim, young Annie, survived. Eighteen years later, Muncie manages to gain a new trial with Annie as the only witness. Muncie proceeds to torture Annie mentally with letters and by stalking her, before trying to murder her. When he is discovered, Muncie attempts to murder the police lieutenant hunting him after taking the man's daughter hostage and revealing he never intends to let her live anyways.
"Quiver": Stanley Dover Sr., aka the Star City Slayer, was the secret main villain. 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.
Brad Meltzer's The Archer's Quest. While it is generally agreed that Brad Meltzer had a good grasp on the characters involved, many fans disliked the revelation that Oliver Queen had been aware of Connor Hawke's existence prior to the two meeting in an ashram and walked out on Connor and his mother when he was born. This was partly due to it flying in the face of Oliver's previous characterization as an lonely orphan who wanted nothing more than a traditional family life with a loving woman and lots of kids and partly due to it requiring Oliver to have been capable of lying to his best friend, Hal Jordan who, at the time, possessed the cosmic knowledge of all of The Guardians Of The Universe minus one and informed Oliver that he had a son with the understanding he was ignorant of that fact.
Andrew Kreisberg and Ben Sokolowski's Kingdom. Even before it started it drew ire simply for following Jeff Lemire's run, which was thought by many to have saved the series from the slump Green Arrow was stuck in after the New 52 reboot. It didn't help that both writers - while experienced comic-book creators - were also writers for Arrow, which has a divisive relationship with the comic book fanbase. The main fear was that they'd turn the comic into a carbon copy of Arrow - a worry that was seemingly confirmed when Kreisberg and Sokolowski dropped most of the book's supporting cast except for John Diggle (a character originally introduced on the show) and introduced Felicity Smoak in the first issue, establishing the Power Trio featured on the show. However, they also attempted to reintroduce several elements of the classic series that had been missing since the New 52 reboot, including Oliver's friendship with Hal Jordan, the character of Mia Dearden and Oliver's mouthy 'man of the people' characterization.
Felicity Smoak's introduction in the above mentioned Kingdom arc was not well-received. This was, in large part, because she was introduced at the same time all of the old supporting cast - which already included two computer experts - were completely dropped from the series. This, combined with the creators gushing about bringing her in, resulted in her quickly being labelled a Creator's Pet by those not fond of Arrow in general or elements unique to the show being introduced into the comics in specific.
To a lesser degree, the villain Cupid, who was created by Andrew Kreisberg during his run on Green Arrow/Black Canary and was also introduced in the Kingdom arc for no reason other than Kreisberg wanted her in there.
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.
Dork Age: The majority of fans are in agreement that post-Justice League: Cry for Justice was one for Roy and Lian Harper, on account of Roy getting his arm severed and Lian getting brutally murdered in order to push Roy into being an angst riddled, drug addicted, psychotic vigilante. Fans loathed this era for how it stripped Roy of everything that made him an interesting character and for how Lian was reduced to a plot device in the worst possible way, especially when DC tried to spin this as a good thing because they thought they couldn't do any good stories if Lian was dragging Roy down. Fan and critical backlash at Rise of Arsenal and Titans: Villains for Hire proved otherwise. Going into the New 52 and Rebirth, fans still argue this is a Dork Age for Roy because while Roy got his arm back, DC retconned Lian out of existence and, with the exception of Convergence, have show no signs of bringing her back or even wanting to bring her back. That's not even getting into how Roy was stripped of everything else that made him unique and reduced him to a prop existing to boost Jason Todd, while everyone seemed incapable of not mentioning his substance abuse problems. While Rebirth tried to restore his old personality and connections to the Titans, it didn't get rid of him being so-called best friends with Jason and everyone still wouldn't shut up about his old drug habits. And then DC Dropped a Bridge on Him and killed him off in the first issue of Heroes in Crisis, followed by offering another retcon on his past addiction by stating he was using prescribed pain meds and switched to heroin because it was safer and cheaper. This in the eyes of many fans is what officially cemented 2010-2018 as one long Dork Age for the character.
Ensemble Dark Horse: Lian Harper's been a fan favorite for Arrow and Titans fans for years, both for what she brought to Roy and as a character in her own right. She's an adorably precocious and energetic kid with a knack for keeping up with superhero name changes, shows great insight into her dad's personality, and overall had one of the best parent-child relationships in the entire DC Universe. Her death in Justice League: Cry for Justice and how it was used to turn Roy into a psychotic anti-hero had many fans seething in rage. While those fans were happy when she was brought back in Convergence, they're also still angry DC hasn't properly reintroduced Lian.
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. The run that follows was disliked, but the creative team brought back the beard, though reception is still very mixed.
Harsher in Hindsight: Ollie's involvement in Dr. Light's mind wipe in Identity Crisis after the latter raped Sue Dinby, given Chris Hardwick, who voiced Ollie on The Batman had allegations of abuse, including sexual abuse, levied against him by Chloe Dykstra.
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).
Dennis O'Neil was the writer who really defined Green Arrow as a character by giving him his signature liberal political stance and his relationship with Black Canary even though he wasn't the one to initially create the character.
Other fans consider Mike Grell to be this, and while he built from Dennis O'Neil's legacy, he was also the one that made Green Arrow Darker and Edgier, starting with Longbow Hunters.
Devin Grayson, and to a lesser extent Jay Faerber, are considered the only writers in the last couple of decades to have any real clue as to what they were doing with Roy and Lian Harper. Devin was capable of referencing Roy's past addiction both for some drama but also some levity, and had redefined his Arsenal persona beyond a stereotypical edgy 90s hero. Jay tried to move past Roy's toxic relationship with Cheshire and had Roy address how Cheshire was never going to change. Both authors properly portrayed Roy's father/daughter relationship with Lian with depth and were responsible for giving Lian a genuine personality beyond being a cute plot device. The quality of every writer who handled Roy after that has either been uneven (Judd Winnick, Brad Meltzer, Dan Abnett), or just God awful (Scott Lobdell, J.T. Krul, Eric Wallace, Benjamin Percy).
Narm: Some people feel Benjamin Percy's dialogue in the Rebirth series, at times, can be summed up as "I want this to trend on social media", because of how awkwardly it inserts certain social issues.
Never Live It Down: Roy Harper's two-issue struggle with drug addiction has pretty much defined the character ever since. Most animated adaptions however, can't look past his beginnings as a Robin Expy.
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.
Following Flashpoint, we also have Ollie and Tarantula, who Ollie starts commenting on how he's falling in love with her in-spite of their on-panel interaction at that point had basically no romantic element, not even any flirting. She disappears as soon as the arc is done though, which combined with other odd things (like Ollie brutally killing some of the Skeletons, at least before they were revealed to be zombies), makes the whole arc a giant Bizarro Episode.
Ollie himself following the Kevin Smith run; Smith established Ollie understood the mistakes he had made prior to his death, be it with Dinah, Roy and so on, and featured him resolving to be a better man and there for his son; cue the next writer and Ollie has cheated on Dinah with Black Lightning's niece, inadvertently caused her death, and the character was generally perceived to be unappealing and a bit of a mess from there on, culminating in the one-two-three punch of Ollie's role in Identity Crisis, the botched approach to the wedding, and Cry For Justice.
Tommy Blake Jr., Cheshire's infant son by Catman and Lian Harper's baby brother, was never featured in any stories involving the Arrow Family or the Harpers. It would've been interesting to explore how Lian would react to learning she was a big sister, plus what the reveal of Tommy's existence might mean for Roy and Cheshire. Considering Cheshire deliberately conceived Tommy as Lian's replacement in act that meant forsaking Lian's life, chances are Roy learning of such callousness would've redefined their relationship and completely changed their dynamic. There were also the possibilities of seeing Roy raising a child he wasn't biologically related to, much the same way his foster father Brave Bow and Ollie raised him. And considering Tommy's biological dad is Catman, it would've been interesting to see how Ollie would react to gaining a grandchild born from a man he detests.