Trivia: To prepare for his role as the Joker, Heath Ledger lived alone in a hotel room for a month, formulating the character's psychology, posture and voice (the last one he found most difficult to do). He started a diary, in which he wrote the Joker's thoughts and feelings to guide himself during his performance. He was also given Alan Moore's comic "Batman: The Killing Joke" and "Arkham Asylum: A Serious House on Serious Earth" to read. Ledger also took inspiration from Alex in A Clockwork Orange(1971) and Sid Vicious.
Trivia: In the restaurant scene, right when it begins with Harvey and Rachel talking, if you look to the bottom right of the screen, Heath Ledger, who is not wearing the Joker makeup, is sitting at a table with someone. [This is up for debate, as it's a strong likeness but not definitively him. Regardless, worth a look.]
Trivia: In the banquet scene, when the Joker and his troop arrive, the man that the Joker says reminds him of his father is Senator Patrick Leahy of Vermont. Senator Leahy is a huge Batman fan and has lent his voice to the animated series and also had another small cameo appearance in Batman and Robin.
Trivia: This marks the second time movie characters adapted from another source have lept off the Two-ifc, the world's third or fourth tallest building, in Hong Kong. (The similar-looking building that Batman enters is the building's shorter and earlier-constructed twin, the One-ifc.) The first was in Tomb Raider: The Cradle of Life in which Lara and Terry Sheridan leap off the still-under-construction building to escape their pursuers.
Trivia: Heath Ledger stopping after the first sequence of explosions at the hospital ends and the tinkering with the remote were actually improvised. The script originally saw Ledger going straight to the bus and NOT wait for the much bigger sequence of explosions.(Apparently the gap between the two sequences was a safety gap for the actor to get away).