As long as it isn't scratched up you can clean it easily.  It is very smooth.  I think that a rougher surface might have those problems, or if there were scratches in the plexi the dirt and grime could get stuck in them and make it stand out.  I think that VRF had a white acrylic version of all the Pixelbox parts made, so maybe he'll chime in.  
It just dawned on me that you may mean frosted white plexi, and sometimes that has a texture and would definitely get dirty quickly.  The opaque/shiny kind is what I was talking about earlier.
This thread begs me to sign off with a quote from the automotive world...
Keep the shiny side up,
Brian