Problems of Schroedinger's "wave-only" viewpoint: (namely the viewpoint that the wave function is a real physical wave and the electron IS the wave function):

• The problem of indeterminism of the "wave function collapse" during measurement
• The problem of multidimensionality of the configurations space for a many particle system
• The complex value of the wave function
• The superluminal wave propagation velocities associated with the "collapse" process (problem of nonlocality)
• The problem of macroscopic limits (for example why wave packets corresponding to macroscopical objects don't spread in space with elapsing time?)

For a detailed description of these problems see chapter 6

Because of these reasons, wave only viewpoint was considered as inadequate and the concept of wave-particle duality was considered as inevitable. The wave function was regarded only as a probability wave namely as a tool to predict the probability of a particular outcome in a measurement. This was a development in the wrong direction

For a detailed discussion see:

THE OBJECTIVIST QUANTUM