Makeup (Symbol)
In the beginning of the film, two bank robbers discuss the Joker's makeup and the fact that it is his "warpaint." In this sense, the makeup is a kind of intimidating mask that the Joker wears to scare his victims, a symbol of his villainy. It also is representative of his status as a clown and a freak. He wears the traditional makeup of a circus clown—normally an uncanny but harmless figure—but it is smeared and wild, signifying his instability and unpredictability. Thus, the makeup symbolizes the ways that the Joker is intimidating and squirrelly.
Two-Face (Symbol)
Harvey Dent's face is burned on one half while the other side remains intact. Not long after the accident, he is corrupted by the Joker and becomes a horrible villain, one who lives his life by the rules of chance. His two faces, as well as his identity as Two-Face, have multiple symbolic meanings. On one level, they represent his fall from grace, the fact that he was once a force for good in Gotham, who has been corrupted by moral ugliness and the desire for revenge. Additionally, they represent his newfound ethic of chance, his belief that the fairest moral equation is one that puts everything to the test of heads or tails.
Joker Card (Motif)
The Joker uses a Joker card from a deck of cards as his "business card" and leaves it for people at various moments in the film. It almost always signifies his intention to kill them, and becomes symbolic of the havoc that he is wreaking on the city of Gotham.
Batman (Symbol)
The Batman himself is an archetypal and symbolic figure, representing the individual who must take justice into his own hands in order to keep people safe. Especially in his identity as the "Dark Knight," he is a misunderstood and marginalized figure who is willing to make large personal sacrifices on behalf of the greater good, becoming a symbol for the hero who does not ask for praise. He is an archetype of the completely selfless and ego-less hero, someone who cares more for society than he does for his own desires.
Social Experiments (Motif)
Throughout the film, The Joker conducts a number of "social experiments," perverse ultimatums that encourage ordinary citizens to commit acts of violence. First, he begins killing people in order to goad Batman into revealing his true identity, then he says that he will blow up a hospital unless someone kills the man threatening to reveal Batman's identity himself. His final "social experiment" is when he fills the two ferries carrying people across Gotham's river with explosives and asks the passengers on each boat to blow the other up before midnight. The Joker's sick games become something of a motif in the film, a testament to his sadistic philosophy and his belief that human nature is inherently ugly and ruthless.