Y0.5Ca0.5BaCo4O7 was recently introduced as a possible candidate for capturing some of the predicted classical spin kagome ground-state features. Stimulated by this conjecture, we have taken up a more complete study of the spin correlations in this compound with neutron scattering methods on a powder sample characterized with high-resolution neutron diffraction and the temperature dependence of magnetic susceptibility and specific heat. We have found that the frustrated near-neighbor magnetic correlations involve not only the kagome planes but concern the full Co sublattice, as evidenced by the analysis of the wave-vector dependence of the short-range order. We conclude from our results that the magnetic moments are located on the Co sublattice as a whole and that correlations extend beyond the two-dimensional kagome planes. We identify intriguing dynamical properties, observing high-frequency fluctuations with a Lorentzian linewidth Γ⩽20 meV at ambient temperature. On cooling a low-frequency (~1 meV) dynamical component develops alongside the high-frequency fluctuations, which eventually becomes static at temperatures below T≈50 K. The high-frequency response with an overall linewidth of ~10 meV prevails at T⩽2 K, coincident with a fully elastic short-range-ordered contribution.