We have explored the magnetic excitation spectrum of the S=1/2 square lattice Heisenberg antiferromagnet, K2V3O8, using both triple-axis and time-of-flight inelastic neutron scattering. The long-wavelength spin waves are consistent with the previously determined Hamiltonian for this material. A small energy gap of 72 +/- 9 mu eV is observed at the antiferromagnetic zone center and the near-neighbor exchange constant is determined to be 1.08 +/- 0.03 meV. A finite ferromagnetic interplanar coupling is observed along the crystallographic c axis with a magnitude of J(c)=-0.0036 +/- 0.0006 meV. However, upon approaching the zone boundary, the observed excitation spectrum deviates significantly from the expectation of linear spin wave theory resulting in split modes at the (pi/2,pi/2) zone boundary point. The effects of magnon-phonon interaction, orbital degrees of freedom, multimagnon scattering, and dilution/site randomness are considered in the context of the mode splitting. Unfortunately, no fully satisfactory explanation of this phenomenon is found and further theoretical and experimental work is needed.