The quasi-neutral hybrid particle-in-cell algorithm with kinetic ions and fluid electrons is a popular model to study multi-scale problems in laboratory, space, and astrophysical plasmas. Here, it is shown that the treatment of ions as finite-size particles and electrons as a grid-based fluid can cause significant numerical wave dispersion errors in the magnetohydrodynamic limit ($kd_i \ll 1$, where $d_i$ is the ion skin-depth). Practical requirements on the mesh spacing $\Delta x/d_i$ are suggested to bound these errors from above.
