I only have a few 1000uF electrolytics, so I put 2 on each rail, same ADC flutter of mostly 1, sometimes 2.
+- 2 counts is as good as it will ever get for raw adc reads on a breadboard, if you right shift 2 bits that's a 256 count resolution that should be very stable

the scope is your friend here , measure the AC noise. every 5mV of noise on the rail and/or the pot wiper is +- 1 more count