This won't be an answer to question, more "food for thought".
Neither the ADC nor the pot is "perfect" (of course) and the ADC inside a $1.50 PIC will not be the best but it does have data specified the datasheet, page 632.
What's the linearity and "resolution" of the potentiometer? There are some mighty fine potentiometers out there but a cheap 10-turn is probably worse than the ADC. In theory, the resolution is "endless" but in practice it is not. 4096 "steps", even over 10 turns, is less than 0.9° of rotation of the wiper, can YOU resolve that accurately?
I suppose you could put an accurate voltmeter parallell with the ADC input and compare the voltage readings with the ADC readings? Does the voltage readings also skip the "647-value"?
Remember, if you have the pot across 3.3V then 1LSB of the ADC is 805uV (microvolt).
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