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.
Big Lipped Alligator Moment: In the same room as Clayface is a prisoner who doesn't seem to be any recognizable Batman villain and his model is too detailed to just be a random NPC. It's the winner of the "Appear in the game!" contest's appearance.
Breather Boss: Combined with Anti-Climax Boss. The very first boss encounter (with a random mook who was exposed to a prototype version of Titan) seems like it'll be a fair challenge... but he suddenly dies from heart failure after a fairly brief amount of time, no defeat necessary.
Counterpart Comparison: A lot of people who have played the game a few years after its release have noticed a coincidental resemblance◊ between Arkham Asylum's high-security henchmen and Bane in The Dark Knight Rises. Inverted, as the incarnation of Bane in The Dark Knight Rises is the more recognizable of the two despite making his first appearance a few years later.
Crazy Awesome: Joker in a nutshell, when playing as him. The guy can leapfrog over attackers, he uses a joy-buzzer and a comical eye-poke in combat and can use chattering teeth bombs in his predator challenges, yet he can still be as Badass as Batman.
Demonic Spiders: Gun-wielding mooks, knife-wielding mooks, and Ivy's plants.
Ensemble Darkhorse: Scarecrow, due to his segments being considered some of the most memorable.
The mooks with stun batons that appear about a quarter of the way into the game. If you don't deal with them promptly and correctly, their batons can quickly whittle your health down to half on the intermediate to higher difficulties.
Arkham Inmates in the DLC map Totally Insane. Remember those crazies who you dispatched with one counter and a ground takedown? Yeah, they show up here alongside lots of thugs. Except now you barely have time to do a ground takedown on any of them. Which means that they keep coming. And that's not the worst part. Said crazies can't dispatched by any of the special takedown maneuvers and will simply leap over Batman. The worst part is that doing so will break your combo and leave you open to thugs, or even worse, more crazies.
While they can't hurt you, the gag teeth do show some elements of this, considering how numerous, omnipresent and annoying they are.
And that they don't show up on either the main map or the ones Riddler leaves lying around, yet are required to finish off Riddler's challenges.
In addition, there's Batman briefly getting infected by the TITAN formula himself near the end of Asylum, but is able to successfully overcome the effects. He wouldn't be as lucky the second time around, this time getting infected with the tainted batch of it mixed with Joker's blood, leading to far more devastating effects on his body.
Hilarious in Hindsight: During the beginning sequence of the game, Frank Boles insults the Joker, who tells him to keep his mouth shut or it'll get him into trouble. Later on in the game, Boles is revealed to be a double agent working with the Joker, and Batman is able to trace him via a scent trail of bourbon he'd been drinking. The Joker finds out and has Boles killed.
With the release of Batman: Arkham City, this particular line, given you encounter the first as a sidequest, the second as part of the main plot and the last in DLC.
Oracle:(exasperated) What now? Riddler? Two-Face? Some kind of giant Joker robot?
When Batman talks to the Joker on a monitor early on, he quips "You were expecting Two-Face?" Not only would Two-Face appear in Arkham City, as stated above, but his voice actor in that game, Troy Baker, would go on to also voice the Joker in the prequel, Batman: Arkham Origins.
In addition, the PlayStation 3-exclusive Joker DLC has the Melee Challenge Maps in which the Clown Prince of Crime you control has lethal laughing gas, a revolver handgun, and the joy buzzer as special attacks, while he uses his impressive hand-to-hand abilities to punch, slap, kick, and poke out eyes. In Origins, you get to do the same hand-to-hand abilities as in Asylum's Melee Challenge Maps while you fight as the Joker in the Comedy Club flashback.
Les Yay: Harley and Ivy get their usual dose of this despite only having one (very short) scene together. Harley lets Ivy out even though she isn't on the Joker's list, and Ivy blows her a kiss as she leaves.
Joker: "I could watch those two all day. What a riot!"
Hearing Joker repeat the same two or three lines over and over and over again as you try to Gold the challenges can get very annoying.
The raspy screams the Lunatics give off before charging you.
Older Than They Think: The Predator gameplay has its roots in the Batman Begins video-game adaptation; in turn, that gameplay was based on Metal Gear Solid's stealth aspects. The heart monitor, grapple-point gargoyles, enemies becoming gradually more frantic as they're hunted, and some special attacks, all made it into Arkham Asylum.
Scrappy Mechanic: Players and critics complained that Detective Mode is just so damn handy, you'll never not want to use it - the downside is that you have to play the entire game in a blueish hue, seeing every character as a translucent skeleton. The loudest complaints came from Rocksteady's own art directors, who were upset that players weren't seeing the game as they intended it to be seen, so they altered the mechanic for the sequel, making it so that certain player interface aspects were unable to be seen in detective mode.
Special Effect Failure: The Sanatorium is apparently the only place on the island experiencing a thunderstorm.
The fight against Poison Ivy mostly has a fixed camera angle. But for a short time at the beginning of the fight, you can look around freely like you normally can. Looking to the sides reveals that the wall that was supposed to be behind you wasn't textured, allowing you to see right through to the skybox.
Squick: During the first Scarecrow segment, Joker asks Batman what his fears are, this would have been fine, but then he just had to say "Me? In a thong!?!"
Doubles as a Funny Moment, as the "Blaaaahahahaha!" that the Joker gives right after indicates that he knows that it'd be more Squick than scary, and that laugh he gives is absolutely hilarious.
During one of Batman's Scarecrow induced hallucinations there's a Batman duplicate ravenously gnawing on a dead rat.
That One Level: Your return later on to Intensive Treatment, where the gargoyles (the key to your superiority over gun-wielding Mooks) have been set to explode when you climb onto them. It's much harder than it sounds, though you can use the Batclaw on the roof of the control room to yank mooks off the ledges and severely whittle down their forces.
Killer Croc's lair.
Saving Gordon from Harley near the end of the Medical Ward. There's virtually no room for error; misalign your position even slightly, you'll immediately get spotted, which results in Gordon getting shot up and you having to start all over. Oh, and if a guard just happens to see a knocked out baddie, that also triggers the game over, so not only do you have to carefully maneuver your way through the guards, you have to make sure you take them out in very specific areas where the other guards can't find them, or you fail instantly. And after you finally manage to escape the guards, you're immediately thrown into a fight with Bane.
That One Sidequest: On your way into the Visitor Center to the final boss, there's a short hallway with 20 mooks in it who won't attack you unless you attack them. Though they're unarmed, so many of them in such a tight space is extremely difficult, even with all the upgrades you have at this point.
Joker Teeth. It might have something to do with them not being an actual riddle, tape, or Arkham chronicle. Also, while about 90% of the teeth show up more or less naturally as a result of the story progression, there's that set that hide above the hallway to the warden's office, which happens after the player has realized this, and then notice they missed them after the sequence is over.