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.
Complete Monster: The Joker is once again presented as an Ax-Crazy psychopath. He beats Batman's young sidekick Jason Todd with a crowbar, leaves him broken and battered in a warehouse and then proceeds to blow up the warehouse. Later in the film, Joker kills four of Black Mask's mooks for no reason, after Black Mask (very reluctantly) freed Joker from Arkham. Joker then attempts to kill both the Red Hood's and Black Mask's gangs by covering them with gasoline and using a lighter to try to set them on fire. Also throughout the movie, Joker taunts Batman about Jason's death.
Counterpart Comparison: A lot of people noted Red Hood's resemblance to Deadpool when the first trailers went online. The similarities are even more marked in the actual film, where the character behaves near-identically to Deadpool in the latter's earlier appearances.
Foe Yay: The Joker interrupting Batman's Tear Jerker speech by saying "aw, so you do think about me!" In the Joker's typically disturbing fashion, he says this while Batman is saying that not a day goes by where he doesn't think about killing the Joker.
Fridge Brilliance: Nightwing and Batman visit Joker in Arkham to see whether he was related to the Red Hood in any way, which he is not. However, his actions caused Jason Todd's death and subsequent transformation into Red Hood after his resurrection, so in a way the Joker was linked to Red Hood in more ways than one.
Fridge Horror: It's almost certain some of the lieutenants Red Hood beheaded were with their families, perhaps at dinner, and were forced to watch his actions.
Ra's al Ghul. Despite his being a ruthless supervillain who, as Batman says, has never shied away from shedding blood, his deep remorse and sorrow over Jason's fate, resurrection, and subsequent rampage are clearly heartfelt and genuine.
And the fact that it's a logical fallacy to say killing the Joker would make Batman accept killing any criminal, when Joker has been the one villain who has never shown any capability of possible redemption in any form, unlike the rest of the Rogues Gallery.
He's also right about Batman not being able to stop crime — how long has Batman been trying without any success? And sometimes he even manages to make it worse.
What The Hell, Casting Agency?: Reactions to John DiMaggio's casting as Joker were... mixed, to say the least. The release of the character models featuring a somewhat burlier Joker eased concerns somewhat. And then the film was released and a lot of those who doubted he could pull off the role did a complete 180.
Audiences were also skeptical of Jensen Ackles playing a lead character, as he had never done voice acting work prior to this film.
And anyone other than Kevin Conroy as Batman raises suspicions. But Bruce Greenwood did a good job, especially as a Batman who's supposed to be a little older than we normally see him.