Batman: Under the Red Hood/Headscratchers

The Joker at the Bridge

 * How come the cops surrounding the Joker on the bridge never try to take him out with a sniper when he's obviously trying to torch people alive? Batman may have a no kill policy but cops do not.
 * Considering it was the Joker, it might have been safer to see what he had planned first. For all they know, he had bombs planted all over the city.

Ra's' Castle

 * How close is Ra's' castle in that Batman managed to fly there and back again in what looked like a single night?
 * He flew there and back in the Bat-Jet- who knows what Applied Phlebotinum-powered feats that plane is capable of.
 * We don't know the exact distance and where Ra's castle was (or even the exact location of Gotham), and regular airlines are restricted to specific speeds (usually just under Mach 1) while Batman can push it as fast as he wants. Normal timetables don't apply.

Jason's Body

 * How come Jason's body looked perfectly fine after being beaten to an inch of his life then blown up? For that matter, how could Alfred have possibly thought that everything was in order after they dug up the grave and saw a body that was hardly decayed when Jason was buried five years previous?
 * Alfred was pretty far away so he might have had difficulty seeing Jason's body in detail.
 * Chalk Jason's condition post-explosion to the censors and wanting Batman to hold a corpse instead of a bucket of giblets. Early footage of Jason's murder had more blood flying around.
 * While 5 years is pushing it to stay pristine, proper embalming can make a body stay in rather good shape for a long time. There are jokes in the industry that they have a guarantee for 30 years on an arm or leg.

Did the Joker find out Batman's real name?

 * After Batman and Red Hood battle their way into Hood's hideout, both refer to each other as "Jason" and "Bruce," before Jason reveals the Joker is tied up in the closet. Judging from the Joker's lines, it looks like the Joker heard their conversation which would then mean the Joker knows Batman's first name is Bruce.
 * I like to handwave it by thinking that the Joker only just came to when the door was busted open and that the Red Hood had already revealed himself to the Joker earlier or that the Joker put two and two together as soon as he saw Jason wearing the Robin mask. Though that still doesn't justify Jason's stupidity in calling Batman by his name when he knew the Joker was there.
 * But Jason's plan was to kill Joker anyway (or have Batman do it), so he likely didn't care what Joker heard.
 * Hell, consider that if the Joker found out who Batman was, Bruce might have felt he had to kill him. I'd say that actually qualifies it as Fridge Brilliance.
 * It could be like in Morrison's Batman run, where the Joker knows but doesn't especially care.
 * If he knew Batman's identity what's to stop him from pressing the advantage and attacking Wayne and anyone associated with him? He already does that to Batman.
 * Because, in the game between the two, that's not fair.
 * I've seen it in a few continuities, but Joker isn't after Bruce. Joker views Bruce and Batman as two separate people. He may even view defeating Bruce Wayne as Batman holding back. I recall an instance or two where they had captured Batman, and Joker's response to being asked if he wanted Bats unmasked was along the lines of Batman being the true face.
 * We have to remember that Bruce and Jason like the rumored first name of Joker, Jack, are very common names. And as Joker never peeks under the mask cause it would for him ruin the game, I don't think he'd do what a more sane villain would and dig into who they are. So knowing their first name doesn't really matter.

Chemical Factory

 * Why was the chemical factory still in operation after the Joker's accident there?
 * Not like the Joker was in any condition to file a lawsuit...
 * Because companies don't just shut down operations after one accident that happened because a bunch of criminals and a vigilante who is also breaking the law fought there. The company wasn't responsible for the accident--standard safety procedures aren't exactly designed to protect people when they're having big fights in the middle of the chemical tanks.
 * Standard safety features such as catwalks over open-topped vats of horrible and apparently volatile chemicals? You'd think they would be shut down anyway.
 * Even facilities that do fail safety inspections IRL are often kept running for a very long time as the owner jumps through whatever hoops they can to stall so they can make as much money out of it as possible before having to shut it down.
 * This is Gotham, Extremely Corrupt Wretched Hive Vice City of the DC Comics universe; the safety inspectors were probably bought off.

Red Hood's Plan

 * The plan relied pretty heavily on Black Mask getting so desperate that he would break the Joker out of Arkham to help take Red Hood down. Why would either Red Hood or Black Mask ever consider that to even be a viable option? The Joker has a reputation in the DCU as being the single worst person to team up with. Hell, even in just trying to get him in on the plan, he killed a handful of BM's men for no real reason before negotiating terms. If you want someone killed, you hire Deadshot, or Deathstroke or anyone else with "death" in their name. The Joker isn't an assasain, so why would Red Hood just assume he would be Black Mask's go to guy? For that matter, why the hell was he?
 * This troper always thought it was the Black Mask going, 'Okay, I'm screwed unless I call in the big guns. And who's got a bigger grudge and less self-preservation instinct against self-named heroes than the Joker? It's not like it'll matter if he dies; he's nuts!'
 * Interestingly enough, Deathstroke did play a role in the comic storyline this movie was based on (since it was a tie-in to Infinite Crisis). He promptly berated Black Mask and sent a group of second-stringers to kill the Red Hood; it didn't work out.
 * Even if Black Mask did call in someone else instead, Jason would have just killed or incapacitated them, not to mention that Black Mask is not made of money; he has limits on how much he can pay someone else to try and kill the Red Hood. Joker works for free and is all around the biggest loose canon in Gotham, which makes defending against him impossible (meanwhile the Red Hood could take precautions against Deadshot, Deathstroke or other assassins, if not just pay them off).