Aside from the obvious "psychological" meaning of the red coat which has
already been pointed out (that is, that it suggests that Schindler
himself is able to see one of the herd in the ghetto as an individual,
and when he/we later see her dead body in a heap of others he/we can see
the whole heap/the whole camp apparatus differently), I always assumed
the red coat was a nod at Eisenstein. One of his b&w films (I think it's
_Strike_ or _October_) contains a hand-colored red flag. They don't
bother to color in the flag in all the prints, but if you've seen one i
think you'll agree the Schindler red coat is eerily similar.
Also, re the earlier discussion of the use of b&w in _Raging Bull_ as
perhaps motivated by wanting to avoid red shift, etc., the documentary
_Visions of Light_ has a segment on _Raging Bull_ in which they talk
about the cinematographer's effort to go after the look of Life Magazine
photos from the 40's and 50's--necessarily black and white. It's a
beautiful sequence; I think they cut back and forth from Life photos to
shots from _Raging Bull_.
Does anyone remember the moment in Hitchcock's _Marnie_ when the screen
goes red? How is that effect achieved?