Hi,
I sounds like the fluctuations in the 5V supply, which is your ADC reference is fluctuating.
The UART and USB IC may be producing noise on the 5V supply when they are transmitting data.
Try a 10uF or 100uF across the 5V pin and gnd of the D1.
Does the D1 have an internal reference you can use instead of the supply reference?
Tom... 
