The mineral buildup is most likely from hard particles that got through your water softener somehow. Have you tested the grains per gallon of hardness since you installed your water softener? I wonder if the water softener isn't working properly.
If you have a little hardness even after your water softener, you could get a water softening cartridge.
http://www.waterfilters.net/Pentek/wholehouse/Specialty_Filters/WS-20BB-Water-Filter.htm
Thank you,
WaterFilters.NET