I tried a simple analogRead of a simple two resistor voltage divider and got "wobble", readings of 512 or 511. Your circuit is much more complex than mine!, so many more sources of wobble.
I think your in the area where real circuits and theory differ.
Possible sources of wobble a 1 part in a 1000 wobble.
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The output from your PS is not as good as you think. If you looked at it with a very good 'scope you will find it varies even with no load, at mains frequency.
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The load is never as constant as you think. A lot of chips draw more current on the rising/falling edge of the clock than in between.
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Ambient light changes, some bulbs flicker at the mains frequency, this may be, just, enough.
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Induction in that 4 meter cable (from near by mains cables) is the cable shielded?
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Small changes in temperature.
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Vibration.
Mark