Say you used 100K pots, and read them out one at a time, you would find that adjusting on pot affected the readings you got from all the others.
Possibly, but I think the effect would be minimal, +/- 1 count at worst. The source resistance seen by a pin when fed from a 100k pot is 25k at worst (when the slider is mid position). Using a 47k pot would give a source resistance of 11.75k maximum, which is only just above the 10k recommendation. OTOH using 1M pots would certainly give noticeable interference between pins.
@antoine1, there are a few ways to use higher source resistance without the readings from different pins interfering with each other:
1. Do each analog read twice and throw away the first reading. Unfortunately this doubles the time taken to read from a pin (from about 110us to about 220us).
2. Patch the library to add a delayMicros call between switching the multplexer to the chosen pin and starting the conversion, right where there is already a commented out "delay(1);" statement. My measurements indicate that a delay of 10us is sufficient for source resistance up to 100k.
3. Add a capacitor from the pin to ground (47nF or 100nF should do the trick).
4. Add your own code to switch the multiplexer to the correct pin before you call analogRead, with a short delay between the two if necessary.