Children
People in the film cannot see the angels, that is with the exception of children who see them and interact with them throughout the story. The symbol is that we must hold on to our ability to see the world through the eyes of a child in order to fully see.
3 & 1
We see three children playing together in the street. We then see a little boy a few meters away from them. The symbol is of the lone boy longing to be with friends, his desire to have friends to share in the joy playing.
Flying
Marion is at the circus practicing her trapeze routine when suddenly the black and white image goes into color. Damiel is watching her when this happens. The symbol is that Damiel desires to be with her and this moment of her flying on the trapeze transforming into colors is a metaphor for how she makes him come alive.
The man and His City
Homer is walking through the bombed out portions of Berlin in search of the city--the places he grew up in--in his mind. The symbolism in this is the effect that war has on the memories of a man, in that he must work harder to find the life he once loved and lived as many of the places he experienced them are now gone.
Nein!
Cassiel sits with a man who wears headphones and is ready to jump off of a building to kill himself. Cassiel touches the man, but cannot get through to him and the man jumps to his death. Cassiel screams, "Nein!" The symbol is the great pain that the angels feel for even one soul that is lost, stolen away from eternity and how deeply it penetrates them.