Due to being a four-game story, there are details (Batman and Joker's Titan Poisoning in City, Deathstroke's sudden appearance in Knight) that won't make sense unless you've played the other ones.
Some plot points require at least some cursory knowledge of the comic books, though the games rectify this somewhat by giving you profiles regarding characters, but still occasionally falls into this trope, particularly in the case of Jason Todd, whose presence was almost completely absent until Knight.
Games with similar control schemes (such as the Middle Earth: Shadow Of X games), usually have small differences in controls that can mess one up. For example, the aforementioned games have dodge on a single press of the button, here it's two presses in a row.
In Return to Arkham, the framerate has a tendency to sometimes stutter ever so briefly, and there were a few minor changes made to the controls. For example, on PS4, Detective Mode is now triggered by L1, and your weapon is used with ZL. It was the opposite in the last gen versions, and these two factors can disorient players who played the games extensively on their old consoles.
The games are one of the darkest adaptions of both the Batfamily and their rogues gallery, so obviously some (especially fans of a Lighter and Softer or outright Campy Batman) are drawn away from them. Each game has a Nightmare Fuel folder for a reason, not to mention that the games don't shy away (they actually zoom in) from Batman breaking limbs instead of just quick takedowns like most movies do.
Another reason is that, while the DCAU ends on a note of hope as does Christopher Nolan's movies, the endings of the Arkham games tend to be far more bitter than sweet, with Batman consistently shown as a Failure Hero and the finale of Knight ends with his secret revealed to the world and the end of his career as Batman, with the DLC implying that his sidekicks pick up and fight the remaining villains. The Arkhamverse Batman ends his career not on a note of triumph or Heroic Sacrifice but in defeat and exhaustion.
Ensemble Dark Horse: The Arkhamverse version of Harley Quinn is one of the more popular secondary villains, going from a supporting role in the first two games, to being the Big Bad of her own DLC, to being fully playable in Arkham Knight. Harley's portrayal in the games also raised to profile of the comics version.
Scarecrow. His nightmare sequences in Arkham Asylum were considered some of the best parts in the game. When he was absent in Arkham City, people were disappointed. This may have something to do with him being promoted to Big Bad in Arkham Knight, where he is subjected to a lot of Adaptational Badass-ery.
Occasionally jumps to Hypocritical Fandom, as people tend to ignore any errors between Asylum and Citynote Such as Hush's and Strange's chararacter bios, while declaring Fanon Discontinuity whenever a Origins event doesn't exactly match a bio in Asylum.
It also developed a low-key one with Spider-Man (PS4) which is also part of the overall meta DC v. Marvel rivalry. A lot of Batman fans dismiss the latter for borrowing from Arkham, while others argue that it's combat and traversal was more creative and fresh than the later Arkham games, while also having a sense of humor and lightness that contrasted against the bleakness of the Rocksteady games. This escalated when Spider-Man PS4 broke Arkham City's record for best-selling superhero game in 2019 despite being a platform exclusive as opposed to Rocksteady's multi-platform release.
Foe Yay: All four games illustrate this in Joker and Batman's relationship. Starting early in Batman: Arkham Asylum with Joker: "Tell me Bats, what are you really scared of? Failing to save this cesspool of a city? Not finding the Commissioner in time? Me, in a thong?!" and that the premise of the whole night was a party Joker threw for Batman. Then continuing in Batman: Arkham City with the increasing phone calls from Joker to Batman, the final death scene with Batman carrying Joker out in his arms, and Joker's swan song to Batman. Given their beginnings in Batman: Arkham Origins when Joker's obsession with Batman begins, including his Red Hood story and his mention of "meeting someone very special earlier tonight", and another song for Batman during the credits. And finally culminating in Batman: Arkham Knight with Hallucination!Joker mentioning over and over again being inside of Batman, the heavy indicators that Joker's death affected him so much that he could never return to normal (not even Talia's death is mentioned that much), and the serenade number Hallucination!Joker performed with a little help from Johnny Charisma. Catwoman even makes a dig at the relationship in Knight, and how Batman should stop mourning him and "find new maniacs". The whole Batman: Arkham Series arguably reads like an overall story of Batman and Joker's relationship.
While all the games are generally well reviewed and well received, the prominence of the Joker as really the primary bad guy among everyone else has been criticized, as it lead to the detriment of other villains having a chance at truly taking stage. But this has been a wider-franchise problem for Batman on the whole, since the Joker is so inherently charismatic that he has overshadowed others for a long time in the comics, the cartoons and avoided doing so in The Dark Knight Trilogy only because of Heath Ledger's death. The Arkham games, being a tribute to Batman in different media, could not help over-representing the already over-exposed Joker.
In most Batman media, the Foe Yay between Batman-Joker is subtext and only becomes relevant to the plot in stories where Joker is the main threat. In the case of the Arkham games, it worked well in Batman: Arkham Asylum because the game's smaller island facility setting, overall Bedlam House atmosphere and the main plot (which is the only time Joker is actually involved at the helm) fits that motif better. But in the sequels, the main plot and threat is Hugo Strange's Protocol 10 (and Ra's Al Ghul's plans for Gotham) and Scarecrow's plans to unleash fear toxin and humiliate Batman. In both cases, the Joker's involvement in the plot, and the time devoted to their relationship becomes a Romantic Plot Tumor since every game ends up offering some commentary on their rivalry and mutual obsession. Origins had a good general plot which advertised the Joker as merely part of Black Mask's general scheme, and comics fans were excited thinking Black Mask was going to be a more prominent villain than he was, only to find out that Origins was in fact about Joker's debut in the criminal underworld and the start of his and Batman's "relationship" while Black Mask gets submitted to a thoroughly humiliating Adaptation Decayending with him being killed off brutally in Arkham Knight's Red Hood DLC, while begging for mercy.
The series and its poor track record with making good boss fights is another example. The original game was criticized for reusing the same bullfight setup with Bane or opting for thug attack waves instead of direct battles for most of its encounters with any other boss fights being deemed lackluster or boring (with the exception of the penultimate battle with Poison Ivy). While City was praised for having the famous Mr. Freeze showdown and more original boss fights, overall it remained a criticism due to the presence of several (albeit mostly justified) Anti-Climax Boss segments. Origins, a secondary game made by a different studio, was widely praised in its handling of boss battles, making it appear to be an inversion at first. However, Knight, with a few exceptions (notably fighting Riddler in a giant robot suit and tag-teaming with Nightwing to take down Killer Croc in the DLC) lacked several proper boss fights while many combat encounters with thugs and Batmobile tank battles filled their place.
Genre Turning Point: For licensed games in general. Before Arkham Asylum, most AAA license titles were movie tie-ins like the Harry Potter games, which adapted the movies rather than serve, as the Arkham games, as an adaptation of the license tailored to the video game medium. Since the success of the Arkham games, most licensed games are standalone games rather than explicit tie-ins to a then-popular movie. While some movie tie-ins do exist such as The Amazing Spider-Man, they are more or less relegated to mobile games, and with the most recent Spiderman PS 4 following Arkham's approach in adapting the license to the game rather than make a movie tie-in. Most famously, where The Lord of the Rings had movie tie-in hack-and-slash licensed games, for The Hobbit, Monolith Studios made a game-centric adaptation of the licensed property, leading to the critically acclaimed Middle-earth: Shadow of Mordor. Monolith explicitly cited Rocksteady as their inspiration noting that it raised the bar for adapting licensed properties by insisting that it work first and foremost by providing entertaining gameplay.
Good Bad Bugs: For both Asylum and City, Batman's quick ground takedown consisted of straddling a prone thug and punching him in the head, but due to the target rolling back and forth while dazed, the combat animation could randomly flip him around and have Batman hit him straight in the pelvisor tailbone. While Origins tried to correct this mistake, it also introduced a variation where Batman leaned down and punched the victim's ribs, which sometimes meant he accidentally shoved his face into goons' crotches. It was finally fixed in Knight, where Batman leaps to the side before striking.
Harsher in Hindsight: How shall we put it? The Joker himself has been a Death Seeker from the very beginning of the series. In Arkham Origins, he tries to shoot himself in the head in order to end it all, but Batman stops him from doing so for reasons he can't comprehend. In Arkham Asylum, after the Joker says, "I have nothing left to live for," he does shoot himself, but with a Titan formula gun to the throat. His "suicide" is very painfully slow, as it takes a year for the Titan poisoning to course through his bloodstream before his death and its nature complete their course at the end of Arkham City, in fulfillment of his deserving to die as a monster, all the while Batman is unable to intervene with him.
The comments section on Destructoid had a Running Gag about which infamous C-list Batman villains they'd love to see in the Arkham games, with the most common target for ridicule being Professor Pyg. Lazlo Valentin would eventually get a sidequest to himself in Batman: Arkham Knight.
Like You Would Really Do It: The Arkham VR game starts off with the death of Nightwing, and near the end Killer Croc takes a bite out of Robin, which few people believed would stick. It also takes place between City and Knight, and is a hallucination/dream sequence.
Love to Hate: This version of Riddler is probably the Dolores Umbridge of the Arkhamverse. So detestable that he makes the main villains seem like pretenders, yet you can't help but pat Rocksteady on the back for making him so vile.
Ra's Al-Ghul is the "Demon's Head" and leader of the League of Assassins. A centuries-old warlord who got his start buying Gotham City and restructuring it into the criminal-murdering "utopia" Wonder City, Ra's found and used the healing properties of the Lazarus Pit to sustain his life over the years, amassing countless resources and soldiers to his League in the process. In the present, Ra's pulls strings to begin his ideas for a mass-genocide of those he deems "unworthy" to live in his planned perfect world, and finds a concrete scheme when approached by the monstrous Hugo Strange. Fully backing Strange's plan to build a super prison called Arkham City that functions as a nightmarish concentration camp to hold thousands of prisoners until they are all wiped out, Ra's continuously tries to convince Batman to join his crusade, even betraying and murdering Strange due to a preference for Batman as his potential heir. If allowed to die in his final appearance, Ra's uses his last words to proclaim how proud he is of Batman for taking steps towards doing what is 'necessary,' and throughout the franchise holds the utmost respect for the hero no matter what animosity comes between them.
Basil Karlo, better known as Clayface, is a theatrical shapeshifter who enjoys manipulating others with his excellent doppelganger skills. Breaking out of Arkham Asylum by tricking a guard into thinking he is an innocent, Clayface then sneaks into the maximum security prison Arkham City, where he makes a deal with the sickly Joker to masquerade as him and keep his troops and enemies under the illusion that Joker is healthy as ever. Clayface plays the part of Joker near-flawlessly, fooling everyone including Batman himself into thinking he is the Clown Prince of Crime, and uses his position to orchestrate a variety of takeovers in the city. During his fight with Batman, Clayface gives Batman one of the hardest of his career, forcing the caped crusader into lethal force due to his deadliness. Not reserved solely to Joker, Clayface also shifts into the assassin Deadshot, gaining Penguin's trust and a stash of guns with the disguise.
No Problem with Licensed Games: Not only are these considered the best Batman games ever made, not only are they considered to be among the best licensed games ever made, they're often placed in the top tier of character action games ever made, period. Related to this is...
Only the Creator Does It Right: Rocksteady Studios developed the Arkham IP and did it so well their popularity exploded. So when Batman: Arkham Origins was announced as being developed by Warner Bros. Montreal — essentially a stop-gap game to fill time while Rocksteady was busy making Batman: Arkham Knight — there was genuine concern about how the game would turn out. However, despite lacking serious gameplay changes and the polish of Rocksteady's games, Origins was well received as an expansion of the Arkham universe, with some consider it to have a very compelling story, dialogue and more varied boss battles than the first two games. Furthermore, Knight's status as a Contested Sequel and the problems and controversy of its PC Port has led to Arkham Origins being better regarded by some.
Part of Arkham Knight's mixed reaction is a whole other form of this; Paul Dini wrote the story of Asylum and City, while another writing team handled the story of Origins; neither of those writing teams were involved with Knight's story, and many fans feel that it's inferior to the eariler stories.
Polished Porting Disaster: Return to Arkham has much better character models and graphics, it adds some new details to the environments, but comes with the cost of an unreliable framerate and downgrading of some other effects. According to some, the framerates are actually worse than before.
Patches seem to have improved the framerates (Although City still has the occasional struggle) leaving only some graphical downgrades which are barely noticeable unless played next to the older versions. At the moment, the remasters seem to lean towards the "Polished" side of the spectrum.
Scrappy Mechanic: The otherwise excellent combat system's biggest problem is that it relies on a largely automatic priorization; it generally does exactly what you're trying to do, but once it decides to attack the wrong enemy, the results can be devastating. Spent your instant takedown on an enemy that is immune to it on your left, while you were actually trying to use it on an armored thug to your left? Martial Artists and the challenge map Shiva boss in Origins are especially guilty of this, but it can happen in other games as well.
More and more critics of the series' Detective Vision have popped up over time. Aside from the occasional Predator Mode fight with enemies that jam your Detective Vision or detect you if you're using it, there's no real disadvantage to just leaving it on 24/7 aside from the game's gorgeous visuals being replaced with an ugly VR-style aesthetic. Later games in the series tried to make the Detective Vision aesthetic less overwhelming, and other games who drew inspiration from it such as Spider-Man (PS4)do leave it on by default without replacing the game's visuals.
They Changed It, Now It Sucks!: There are quite a number of fan who hate the brighter, more comic book-esque character models used in the Return to Arkham PS4 port of the first two games, especially in the case of Asylum, feeling that they don't fit the mood of the games.
Two-Face is considered by many to be the most underutilized villain throughout the series, as his role in each game is pretty insignificant. In City he's only there to capture Catwoman so Batman can rescue her, and later get beaten up by Catwoman after the main story ends. Knight is a bit better about this, as his split personality is brought up more and portrayed in a sympathetic manner, but his side-mission is one of the shortest ones in the entire game. One can't help but feel that had he not been mentioned in Asylum his origin story could have been a nice subplot in City, as he could easily have been written as an ally in the fight against Arkham City, and have Hugo Strange slowly break Harvey during the game and bring Two-Face out as an attempt to break the Batman.
Black Mask is built up as this poweful Starter Villain for Batman with both the mob and the cops at his payroll. He is taken out by Joker offscreen who then takes over his organization. While seeing his downfall throughout the series is kind of cool, he never really got a chance to be the cruel badass he is in the comics, as he tends to be resident Butt-Monkey of tye Arkhamverse. Knight's Red Hood DLC implies that he is slowly managing to regain his former power, but gets killed by Jason before he really gets anywhere.
Dick Grayson is the most uninteresting of the three Robins, as he first appeared as a quiet DLC character in City, and his personality doesn't come up at all.note To be fair, City's credits imply he was meant to have a speaking role. Like Harvey above, he gets a better role in Knight, but it's still pretty small. (At least he can talk in Knight.)
Talia is stated to be Batman's true love in this series. However, she's got maybe ten minutes of screen time across all four of the games and their relationship is never really actually developed.
What Do You Mean, It's Not for Kids?: It's made perfectly clear that this game series was not aimed at children, with Arkham Knight even getting slapped with an M rating, but that didn't stop kids from purchasing it. The series is full of brutal death, intense violence, psychological horror, sexual content, corruption, and of course Batman and his villains acting more nightmarish than ever before, all packaged along with extremely dark themes and storylines that can be chilling from their concepts alone. There's a very good argument to be made that they are the darkest Batman adaptations ever made. Unfortunately, there were still some families that thought it was okay to buy for kids simply because it had Batman. Needless to say, people were shocked.
There's also the matter of Troy Baker and how many different characters he plays- first he's Two Face and Robin in City, then Joker in Origins, and then the Arkham Knight/ Jason Todd in Knight. That's overall five different characters done by one actor, which had several fans aghast, especially since Baker has appeared in nearly every major video game released in the past four to five years.