The Klein Gordon equation in its original interpretation suffered from problem of negative probabilities. After quantum electrodynamics was successfully formulated, the second quantized Klein Gordon equation was shown to give a consistent formulation for spin zero particles. WHO DID THIS WORK?
Pauli, with Dirac, Jordan and Heisenberg, had been one of the founding fathers of quantum electrodynamics and, more generally, of quantum field theory. This was in 1928.... One year later Pauli has shown (in a paper with Weiskopf) that a second quantized form of spin zero Klein Gordon equation as a satisfactory as spin \(\frac{1}{2}\) Dirac theory. At the same time this paper also showed that Dirac's argument for choosing a multi-component wave function had to be revised. This profound analysis eventually led Pauli to his famous spin statistics theorem of 1940.
Quoted from Charles Penz," Pauli and Development of Quantum Theory" in
Wolfgang Pauli. General Principles of Quantum Mechanics, Translated by R. Achutan and K. Venkatesan. Allied Publishers Ltd, Shivaji Marg, New Delhi, english edition 1980 edition.