You seem to be experiencing cross-talk between the analog channels. This
happens because all the channels are funneled by an analog multiplexer
into the same sample-and-hold capacitor. If the source resistance is too
high, then the capacitor does not have enough time to charge to
the voltage of every channel.
Here is what the datasheet of the ATmega328P says about the
The ADC is optimized for analog signals with an output impedance of
approximately 10 kΩ or less. [...] The user is recommended to
only use low impedance sources with slowly varying signals, since this
minimizes the required charge transfer to the S/H capacitor.
The problem can be mitigated by reducing the source impedance using a
capacitor at every pot wiper, or by giving more time to the
sample-and-hold circuit: make many dummy readings before the one reading
you want to keep. The proper solution would of course be to replace the
pots with 10 kΩ pots.