Fridge Brilliance: Dent's coin, which is in fact a Two-Headed Coin: He flips it several times, as if to make a decision based on the outcome (at one point conning Rachel into agreeing to go out with him if it comes up Heads). The coin always comes up heads because Harvey Dent always does the right thing. Tails isn't an option. It's only when he becomes Two-Face, and one side of the coin is defaced that any other outcome becomes possible for him.
A lot of critics referred to the film bordering on tragedy; the structure of the film makes a little more sense if you keep in mind the traditional five-act arc of Shakespearean dramas, in which the climax comes earlier than a traditional three-act arc and ends on a lengthy, melancholy resolution (in this case, Dent holding Gordon's family hostage).
During the scene where Batman interrogates Joker, Joker cautions him that striking the head first makes the victim fuzzy. Minutes (and several head-slams) later, he gives Batman the correct addresses, but mixes up the hostages. Though the Joker gave him a Sadistic Choice and intentionally mixed up the addresses, it could almost be Black Comedy. He did warn Batman that the victim's head gets fuzzy…
Bearing in mind that the Joker does things like this adds an extra twist to the scene with the two barges. What would have really happened if someone had pushed their detonator?
During really tense moments (such as when Batman is interrogating Joker), the soundtrack takes on a a high pitched tone, automatically making the viewer nervous.
In the climax, Batman tells Harvey that Joker chose him because "he wanted to prove that even someone as good as you could fall". So, in other words, Joker wanted to bring one of Gotham's best people down to his level. Sound familiar? The only difference is that this time, The Bad Guy Wins.
That's not all. By doing so, Joker indirectly made good on his promise of forcing Batman to break his one rule.