Sometimes the best scenes arise from unscripted improv!
1) As the Joker (Heath Ledger) waits quietly alone in jail after having been arrested by Jim Gordon (Gary Oldman), Mayor Garcia (Nestor Carbonell) shows up to look over Gotham’s latest scourge. While there he also promotes Gordon to the position of Commissioner.
As the officers in the room applaud the announcement Ledger begins, unscripted, to slowly clap – never changing his facial expression. It was just a simple improvisation but one that was unsettling and darkly brilliant.
2) Originally, the Joker (Heath Ledger) was supposed to walk down the street while the explosion at the hospital began, get on the school bus during the scripted pause, and the bus would drive away while the explosion finished.
However, Ledger stopped walking during the pause and in a moment of improvisation began fidgeting with the remote detonator in a very Joker-esque manner – bringing a slight amount of dark humor to what would have just been a serious scene.