Awesome Art: Say what you want to about the writing, but the art is amazing, both Lee's interiors and Miller's covers. The art is what's been selling the book. All the critics who absolutely hated the writing said DC could do the fans a better service by reprinting the books with blank speech bubbles.
A lot of events in the comic go nowhere and have no importance to anything except for Padding. Black Canary, Catwoman, Batgirl, Vicki Vale, Jimmy Olsen, and the Justice League, all feature in the series, but across ten issues they each get about two or three scenes in which they do little, if anything, of relevance. It's particularly egregious because the series is supposed to be about Batman and Robin, but Miller keeps cutting away to other characters.
Bile Fascination: The whole reason the book continued selling: once word about it began to spread, people who haven't read it yet just can't believe it's that bad.
Crazy Awesome: What a lot of Batman's actions appear to be intended as. Unfortunately, he ends up looking just plain crazy.
Darkness-Induced Audience Apathy: When both your protagonists are at best sociopathic jerks without sincere empathy for other human beings, it's hard to feel genuine sympathy.
Designated Hero: Batman. He's psychotic, unstable, and an-all round Jerkass. He kidnaps the twelve year old Dick Grayson, age twelve, forces him to live in the Batcave alone (and expects him to hunt the rats and bats in there for food), and then complains about having him around and physically assaults him. He goes out on patrol laughing about how awesome he is as he gleefully poisons criminals, sets them on fire, and attacks police officers; while it isn't outright stated, Fridge Horror implies many of them don't survive. And he thinks that if he had a power ring like Green Lantern, he would use it to enforce his will on the world and exile Superman from Earth. For some reason, readers are supposed to like him.
Alfred, for refusing to put up with Batman's crazy crap.
Hal Jordan, for calling out Batman on his terrible treatment of Dick Grayson, age twelve, and being pretty much the only hero that doesn't do or say anything stupid or offensive. Ironic given Frank's opinion of him.
The close up on Vicki Vale's panties reveal that the design is that of a Bat. This, much like Vicki Vale herself, has no real importance to anything.
When Dick Grayson, age twelve, is huddling alone in the Batcave, his shadow cast on the floor forms an "R." It's probably supposed to foreshadow that he's going to become Robin, but the Batman mythos is so deeply ingrained in popular culture by this point that it's unlikely anyone reading the book wouldn't already know that.
Harsher in Hindsight: The 1994 Batman/Spawnnote also written by Frank Miller crossover had Batman riled up at Spawn's lethal methods, vexing him to the point where he chucked a batarang in Spawn's face when Spawn asked to shake hands. At the time it was understandable; in Batman: The Dark Knight Returns and Batman: Year One he never used lethal force. After his child abusing, cop-killing antics in All Star Batman his attitude towards Spawn killing seems flat out hypocritical. However, it's completely in line with Miller, as Spawn asks Batman why not kill her - and Batman can't think of anything. Face Palm.
Likewise, a lot of scenes from Year One. Especially the scene early on where Bruce breaks out of a cop car but winds up crashing it and still goes out of his way to save the two unconscious cops inside, even one of which is shown to be somewhat of a dick because of his willingness to let Bruce bleed to death, in light of the cop-killing scene early on in ASBAR.
The love scene between Batman and Black Canary also count. In the story, they make out while keeping their masks on. The scene might be Squick, sexy, or even outright funny to some people. Fast forward three years later, Batman and Catwoman have SEX with their masks on. The scene is here if you want to check it out (NSFW)
As Linkara pointed out, Frank Miller once said he considered Batman the most pure and good of all DC superheroes. Fast forward to this comic and suddenly we have the Goddamn Batman smirking gleefully as he slams the Batmobile into cops, abducts Dick Grayson, Age Twelve, and generally runs around acting so brutally out of character Linkara dubs him 'Crazy Steve' because even Batman In Name Only is still too much like Batman.
When 12-year-old Dick Grayson, age twelve, initially creates his costume with a hood, Batman cynically tells him to drop it, since according to him, this would be impractical in a fight. Flash-forward to Grant Morrison's run, when Damian Wayne becomes the new Robin. His costume includes a hood. Linkara has theorized Morrison might have done this on purpose as a Take That to this comic.
This is acknowledged in the comic itself. Dick mentions how Batman taught him that a hood would limit his line of sight. But Damian proves that, having been trained from a far younger age than Dick, he can fight perfectly fine with the hood.
Idiot Plot: A lot of the story would be over fast if Superman or Green Lantern didn't act like morons.
Memetic Molester: It's often been pointed out that the way Batman treats Robin can get really uncomfortable. Says he's been watching him before Robin was orphaned, takes him away without the kid's consent, smiles as he thinks about putting the kid through hell...
"Fast hands, my little Robin. Fast hands, big mouth."note He's talking about how quickly Robin painted a house yellow while complaining all the while, but still...
Older Than They Think: Some readers take exception to the Joker being emotionless and grim, a far cry from his usual depictions. However his early Golden Age appearances did have the Joker as a more morose character compared to how he would later become known.
Padding: The series suffers from this. One critic noted the book felt like Miller was spreading 4 issues of story across 20. To put it in perspective, Batman meets Dick Grayson, age twelve, in Issue 1. They arrive at the Batcave in Issue 4. The time in between (the entirety of Issues 2 and 3) is focused on either inner monologue which repeats itself or scenes focusing on other characters (despite this being a book about Batman and Robin). Black Canary's introductory scene takes up half of Issue 3, but all that happens is her getting harassed and her beating up a room full of people.
Signature Line: "Who the hell do you think I am? I'm the Goddamn Batman."
So Bad, It's Good: The fact is that most people think this is a bad Batman story; that doesn't stop them from finding it absolutely hilarious.
Stealth Parody: Some people speculate the comic is intended as this. Though debatable, once you read the comic it is possible to see where they're coming from. Everything is so over the top, edgy, dark, etc. that it's kind of hard to take seriously. The fact that Frank Miller has proven long ago that he can write the caped crusader very well also leads people to think he was trying to write a parody. The fact that he's also wrote stuff like Holy Terror just blurs things further.
Strawman Has a Point: When Green Lantern confronts Batman, he points out that Batman is hospitalizing people with his excessive violence and endangering a boy as young as Dick Grayson, age 12.
What an Idiot: Had Green Lantern had a brain cell in his head, he'd have dismissed Batman's offer to meet him at a time and place of his specification, and just captured him then and there with the power ring on his own terms.