The front veneer should extend the drawers a little (0.2mm) on three sides to hide the gap between the drawer and the rails and dividers.
Sanding the sides:
I use a piece of 0.2mm brass to ensure same distance on all sides. The sandpaper is attached to a piece of plywood with doublefaced tape. Such a block is flat and last for very long time. When filled with dust a blow of compressed air brings it to life again.