Mesh size definitely plays an important role, for determining the maximum frequency that can be simulated and also how well a 3D object can be represented, like a sphere.
Even at PML boundary conditions there will be reflections, albeit smaller, so you need to make sure that your simulation domain is large enough to keep reflections at a minimum. Keeping Observation areas away from boundaries is generally a good idea because of these reflections.
From my understanding as long as the time step is meets the Space-Time Stability conditions, a smaller spatial mesh will result in higher accuracy.
http://fdtd.wikispaces.com/The+Space-Time+Stability+Conditions