First off, don't wash it in a dishwasher every time. (That goes for bottles too.) Hand washing gets it much cleaner, but the dishwasher sterilizes it. Also, the dishwasher usually fails to get the grease from nipple soothing creams off the pump.
If you still seem to be having a soap scum problem, it's probably not soap scum... it's hard water. Get a water softener. There are a bunch of options. Check out this website for a list of methods to soften your water: http://www.hardwater.org/water_treatment.html
at 7:43 PM on Dec. 28, 2008