Full spoilers follow.
The Joker's real target. The bank robbery, the mob's money, even Batman's identity are all misdirection. Once the Joker has the city's attention, he abandons the mob entirely — burning his share of the money to prove he cannot be bought — and reveals his actual objective: corrupting Harvey Dent, Gotham's legitimate hope. Everything before that is an elaborate setup to isolate Dent emotionally.
The trap that breaks everything. The Joker allows himself to be captured, which is how he gets access to a cell phone bomb inside an accomplice and, more importantly, how he sets up the film's cruellest choice. He gives Batman two addresses and reverses them: Batman races to save Rachel and finds Dent; Rachel dies in the explosion, and Dent survives with half his face burned away. The choice Batman thought he was making was never his to make.
Alfred's concealment. Rachel's letter to Bruce — explaining that she had chosen Harvey and that Bruce may never be free of Batman — is destroyed by Alfred rather than delivered. Bruce spends the ending believing Rachel would have waited for him, which is itself another protective lie, mirroring in private the public lie Gordon will tell.
Dent becomes Two-Face. Working on him in the hospital, the Joker offers a philosophy rather than a plan: he is an agent of chaos, and chaos is fair. Dent adopts it literally, flipping his now half-scarred coin to decide who lives, and works down a list of everyone complicit in Rachel's death — corrupt cops, mobsters, and finally Gordon, whose son he holds at gunpoint on the same building where she died.
The ferries. The Joker's climactic experiment gives two boatloads of people the detonator for the other. Both refuse — most pointedly a convict who takes the trigger from the warden only to throw it out the window. This is the moment the Joker's thesis is disproved by the very people he considered the most disposable, and it is why Batman can tell him he has lost even as he hangs upside down.
The surveillance machine. Batman converts every cell phone in Gotham into a sonar imaging network to find the Joker, handing sole control to Lucius Fox, who calls it unethical and agrees to use it once. It self-destructs when he enters his name, and Fox — who had resigned in principle — is the one who ends it. The film gives Batman the win and then immediately takes the weapon away.
The ending and its hidden meaning. Dent dies in the fall from the building. Batman realizes that if Gotham learns its white knight murdered people, every conviction Dent won and every hope he created dies with him — the Joker would win posthumously. So Batman takes responsibility for Dent's murders, and Gordon destroys the Bat-signal and orders the manhunt. The film's final irony is that Dent's own line comes true for the wrong man: Dent dies a hero in the public record, while Batman lives long enough to become the villain — by choice. The 'dark knight' of the title is not a brooding hero but a knight in disgrace, whose defining act is accepting a reputation he does not deserve.