Note that the impedance of the analog pins is significant - there is capacitance associated with the
pin, the analog multiplexer and the ADC itself.
The DC resistance can be considered infinite, but the settling time of the ADC depends on the
source-impedance of the thing driving the pin. If that source impedance is greater than around 10k,
you start to see slight errors when switching between different analog pins (ie analogRead called
on several pins in succession). You can either cure this by doing two reads in a row on the same
pin, buffering the signal source, or adding a capacitor to ground on the pin itself, 10nF or so.