Just a few quick measurements, driving LEDs at 3mA via BS170 FETs (1.7Ohm on-resistance at Vgs=5V). I switched the Arduino pins from high-outputs to low-inputs (pull-ups disabled) and measured the time response of the FET drains.
- Without pull-down resistors on the FET gates the LEDs get stuck essentially indefinitely. The Arduino input impedance is extremely high.
- Without pull-down resistors I could cause the LEDs to change state without touching them.
- With 10MOhm pull-down resistors on the FET gates the LED response is delayed by 1ms (WRT the pin state-change).
- With 10MOhm pull-down resistors I could cause the LEDs to change state but had to try quite hard (holding one hand near an AC motor and touching the FET gate with the other).
And the highest frequency which was clearly visible as flickering (to my eyes) was 35Hz.
10MOhm seems a good compromise to me. It's moderately resistant to low-level interference, whilst causing minimal disturbance to ADC input readings.