Dual Identity
We see Jack Napier walk to a mirror with his lover behind him at the beginning of the film. It is a symbol that Jack has a dual identity that has yet to be revealed and the image of the mirror reflecting Jack's image represents this.
Glass on Craps
Bruce Wayne tosses a pen away and Alfred picks it up. Then sets a champagne glass on the edge of a craps table and it would have fallen if not for Alfred grabbing it before it hit the floor. The symbol is that Alfred has, for a lifetime, been looking after Bruce and cleaning up for him as he does not function in the real world very well.
Joker's Hand
After being dropped by Batman into the chemical sludge we see a hand emerge from beneath the surface of the liquid. The hand is white with green fingernails. It is a symbol that Jack Napier has been changed into the Joker and the starting point for his brand of chaos emerging into Gotham City.
Slime Surgery
We watch as a surgeon unwraps Jack Napier's face after he comes out of the chemicals he fell into. He expects that he will be cured. There is brown sludge coming down from the ceiling on the walls which is a symbol that he is using a doctor that will not cure him as it's in a dingy slimy facility with an untrustworthy surgeon. Thus emerges, The Joker.
Purple Smoke
In the museum we see purple smoke begin to pour from the ventilation ducks and as people breathe it in they pass out. The symbol of the smoke is that the Joker is taking over the city as the smoke we've seen up to this point has been white in color.
