I have looked at the board. It appears the diode clamp we have on the USB VBus pin on this board is clamping at a bit higher voltage than normal. This is allowing the voltage to go high enough to cause the clamping diode on the input pin of the main processor to start to conduct. This causes the Vcc line to rise slightly above the nominal 3.3v which is also used as the A/D reference. This causes the A/D readings to be slightly different when USB is plugged in versus when USB is not plugged in. The fix is to replace the external clamping diode to prevent the processors clamping diode from conducting.
Unfortunately I dont have any in stock. We currently have a parts order in that should be here sometime next week which has the diode I need.