What was wrong with Schroedinger's interpretation of the wavefunction?

I've read in a couple of different places, and was told when first learning about quantum mechanics, that Schroedinger interpreted the wavefunction as being representative of the charge distribution of the electrons in a system. This idea was later replaced by Max Born's interpretation of the wavefunction as the probability density of the electrons in a system which is the common view now.


It's quite apparent that quantum mechanics is built on this idea of probabilistic interpretations, and so without it QM would have problems. It's not obvious to me, however, how one makes the jump from interpreting the wavefunction as a charge density to a probability density. Or maybe a better question to ask is this: why did Schroedinger interpret the wavefunction as a charge density? Specifically, what physical motivation is there for this interpretation? Furthermore, in what situations does this interpretation fail? I could imagine some problems with Pauli Exclusion, but perhaps not. In that case, one would still give as an axiom that the wavefunctions of fermions are anti-symmetric upon particle exchange and then one would have that there could be no charge density in that region of space, and everything might still be fine...


So, to narrow things, in what situations does the interpretation of the wavefunction as a charge density fail?


