This is something interesting I discovered today.  I am using a Digitech Harmony Man, which has an effects loop for triggering off of the dry signal, and placing the harmony effect after the distortion.  I ran my signal into the Harmony Man, and went from the loop into the HD500's input.  The FX send went to the Harmony Man's return, and the HM output went to my other pedals, and then into the HD500's fx return.  In this setup, the harmony effect was very thin and digital sounding, like a cheap octave splitter.  This only occurs when the harmony effect is engaged.  Bypassed, everything sounds like it should. 

When I ran everything inline, with the harmony man in front of the POD, with my other effects in the harmony man's effect loop, the pitch effect was much fuller, the way it should be. 
I realize that this is not a common setup, and I doubt many other people would run into this type of situation, but I think there may be a glitch in the HD500 fx send causing a phase issue that thins out the tone.  I will have to take my rig into the studio and compare waveforms to confirm this, but that's what my ears are telling me.  I did keep my GE-7 in the POD's effect loop, and there were no problems there.  The problem is likely in the way the Harmony Man's send and return match up with the POD's effect loop.  Anyone else run into phase problems with the fx loop?