Secondly, the bounty is EXTREMELY exaggerated, and Batman isn't that intimidating yet; he's been just on the game for two years, and most thugs don't even believe he exists, plus Gotham is still pretty much in Black Mask's pocket. Black Mask wouldn't waste that much money when he's still on top of the game, even if he was Dangerously Genre Savvy.
There's also the ludicrous amount of explosives under the bank, too much to just rob a bank. And why would Black Mask even rob a bank by himself, or at all? But remember the trailers: Joker set up explosives across various buildings, just to mess with Batman.
Black Mask wouldn't kill Loeb, but Joker only cares about spreading chaos. He wants to kill Batman out of Roaring Rampage of Revenge, and only Joker would be crazy to throw in 50 million dollars to cause mayhem through Gotham.
This game also explains some of Joker's alliances in Arkham Asylum and Arkham City. Why he's so friendly to Killer Croc? Because Croc worked for him before (It's unclear if he knew Joker had traded places with Black Mask, though).
He considered offing Calendar Man just because it was Christmas Eve. That really sounds like something The Joker would find funny.
The game marketing campaign made extensive use of the phrase "Your enemies will define you". After playing the game it is pretty obvious it was not only about Batman. Bane and specially the Joker were defined by the events of that Christmas night.
Penguin claims that all arms deals taking place aboard the Final Offer are completely legal, due to the vessel technically being property of the Somali government, and thus a small bastion of lawless foreign territory; while he is correct on that count, the police are still able to go after any of his customers for smuggling weapons into the United States. Not that he cares.
Why wasn't Deathstroke killing thugs?
Maybe it is because he consider them pathetic and not interesting in killing as in Batman. Remember one of his line at the start of his combat challenge: "Amateurs. Great".
Another possible reason: he's a merc. He can't profit from their deaths.
There have been previous interpretations of him that will kill their assigned target and nobody else. At least, not without a bonus.
Batman finds Bane's hideout by following a tracker he planted on him back at the hotel. Bane's Venom delivery system was damaged there as well. Bane found the tracker when he repaired his delivery system.
Something that people have complained about is how the combat is less forgiving than the previous games—thugs are faster, counters require quicker timing, etc. But it makes sense for them to be like this in this game, which takes place in Batman's second year, and is about 5-7 years before Asylum. That's about 7-9 years of fighting Batman, who won't hesitate to snap their bones, beat them into submission, use specialized weapons, or use the environment against them. The thugs in Gotham City are a clear, yet still effective, case of Dented Iron by the time Asylum happens.
Critics question why Batman is more prepared or has the same/better gadgets as in other games. Well:
Batman can fly back to Batcave, something he couldn't do in the earlier games.
The plot of Arkham Asylum has Batman underprepared and forced to improvise the entire game with his gadgets because he is caught off guard by Joker.
In Arkham City, Bruce is thrown into the mega prison without any of his gear, and has to have it all flown in, even making extra requests when the situation called for it.
Batman created the glue grenade, which is functionally identical to the Freeze Grenade, but keep in mind that the Freeze Grenade wasn't his invention, Mr. Freeze gives it to him to help him take down the Joker.
The Accelerator actually is not as good as the Grapnel Boost. The Boost is probably an upgrade of the Accelerator.
The remote grapple is similar to the line launcher but not as effective because it can't hook to any surface like the line launcher.
So it isn't so much of whether or not this equipment still exists during Asylum and City, it's a matter of whether or not Batman felt like he actually needed to take it with him. Just like how he switches from heavy metal armor to the sleeker, slimmer suit. (Real Life development choices notwithstanding.)
People claim that Harley's interview with the Joker retcons what had been established in Batman: Arkham Asylum, but thinking about it, it helps make sense of some of the oddities:
Why would Arkham's staff let a an inexperienced intern provide therapy for the inmates? Harley wasn't completely inexperienced at the time, having worked for Hugo Strange's clinic and Blackgate Prison (which justified her interviewing the patients), but she was still hopelessly naive, which the Joker took advantage of.
Why would they let anyone interview the Joker, given what he tends to do? He was still new to Gotham, so nobody knew what he was capable of, and since Harley appears to be transferred to Arkham in the final cutscene, she might have been among the first to interview him.
The fact that Deathstroke is playable in Challenge Maps seems odd, given that previous characters have either been Batman's allies (Catwoman, Robin and Nightwing in Arkham City) or the Joker in a (somewhat canonical) prequel to the events of Batman: Arkham Asylum. However, given that the Challenge Maps in this game are a simulation (being accessed from a computer in the Batcave), we can see the Deathstroke maps as a way for Batman to study him in preparation for a fight (since he knows Deathstroke is after him, but not when he'll attack). It also neatly explains how Batman is able to counter everything Deathstroke throws at him - he's already prepared.
During "Cold, Cold Heart", when Penguin declares that he's going to freeze to death and Batman says that's not his problem, it was initially a bit confusing considering his general stance on saving the lives of the people he fights. It is possible to explain it with him thinking he would have enough to time to go back and save him after the ordeal with Freeze. There's another explanation though; Penguin was frozen with Victor's brand of cryogenic weaponry, which Batman states puts its victims into cryostasis. Even if Batman doesn't save him, he's not going to die.
At the start of "Cold, Cold Heart", there's a mention on the radio of a scandal involving the mayor, which is followed up in the end credits with an announcement of Mayor Hill resigning. This must be the 'one secret that puts all the others to shame' that Enigma mentioned after Batman stopped his blackmail operation.
Joker's Multiple Choice Past has a constant, as Strange pointed out: Batman was always responsible in some way. Then Origins came out, and it's revealed that Joker found his purpose in life: fighting Batman. That was when Joker was really "born".
In Batman: Arkham City Firefly, one of the world's greatest assassins, isn't present despite the game saying that all of Gotham's criminals are imprisoned in Arkham City. Like the Joker entry above, Origins provides some answers: he's either used his contacts to flee the country after the escaping from prison, in Batman: Arkham Asylum there's a newspaper stating as such in the medical center, or he's been recruited into the Suicide Squad.
Listen closely when Bane shouts in his last boss battle. It's a distorted scream of "WAYNE!". Even as a rabid animal, he still remembered that Batman is Wayne until he was electrocuted into unconsciousness. What if Bane had been just a little more resistant to TN-1 and started shouting "WAYNE!" intelligibly?
After Batman finds his hideout, he sets off an explosion to destroy Bane's computer. We don't see Batman planting an explosive, so he must've detonated the tracker. If Batman was willing to kill, Bane would never have left New Gotham, let alone reached his hideout.
The game implies that Calendar Man is busy killing a judge while you're running around Gotham. And there's nothing you can do about it.
Mayor Hill resigns in "Cold, Cold Heart", likely due to Enigma's final secret. This helps rout out some of Gotham's corruption and helps bring Gordon to his eventual role as Commissioner. It also means that Enigma was right when he said exposing Gotham's top citizens was better than Batman's methods.