i dont think it is a major concern, but if you wanted to clean your distiller, and then double or triple distill some water, that should be plenty. i used my tap water one time through.
i have found the distilled water at walmart tests out clean enough for me to make Colloidal Silver with. other brands have not done so, including walgreens.
as cheap as it is, you might clean your distiller real good and then distill some store bought distilled water. if you wish to test it, use an ampmeter with a power source of a nine volt battery. with your elecrodes in the water, if you draw less than 0.50 milliamp, that water is really clean. i find that a rise in conductivity of 1-1.5ma gives me approximately 10ppm of silver metal in suspension. under a half a ma is indicative of any one thing that might be in the water is in the ppb range.