If your adc is an 8-bitter, you need your analog power supply and, particularly, your reference, to be no noisier than 1%. That means that, under full load and maximal external perturbation, the variation on the supply is still less than 5 mV.

If you're using a switcher, you'll never get there. If you're using a "typical" supply distribution circuit for your MCU, you'll never get there.

If you start out with a linear power supply that has no more than 100 ppm of extraneous noise (diodes, load effects, line effects, etc.) under full, albeit resistive, load, then you have a chance ...

I'm not sure what a low-pass filter will do to help your specific situation. No amount of filtering will undo what the power supply does to your circuit, however, unless you take extreme care to decouple a portion of the power circuit from the rest of the device.

I'd start out by powering the device from a hefty linear supply with ultra-fine line regulation and equally precise load regulation. While 5% is adequate regulation for most digital stuff, the impact of that 5% number is the mean voltage it regulates, and not the degree to which it regulates it. Most voltage regulators are simply emitter-followers. The older (e.g. LM340) regulators, not LDO's, use a darlington input stage, which gives them the ability to respond to perturbations much better than LDO's. Unfortunately, that makes them less than desirable for battery-powered applications.

If you simply want the output from your POT to be reasonably stabile, you need to spend a bit of time looking at the ends of the pot with your oscilloscope and the system running. If it's "dead-quiet" with a "dead-quiet" power supply, then you know where your effort has to be directed. If there's HF noise at the ends, then there'll be HF noise at the tap. Take a careful look at that noise, if it's there, and see whether you can determine its source (crystal oscillator, relays, other switching noise, Vcc rubbish on the analog supply.

Once you have the circuit performing as you wish with a "known-good" power input, try the target supply. Often, a low-value (30-50 ohms) resistor between the global supply and a noise source particularly if you can do that on both power and GND, will quiet down the global Vcc, provided both sides are appropriately capacitor-bypassed. One thing that you can try, if you have an all-metal divider (the thing that looks like a drawing compass, but has the metal points at both ends) and a spectrum analyzer, is to find the circuit regions that need more decoupling is to connect the analog GND to various points in the digital circuit with the divider and see how much the interconnection reduces the HF noise. The spectrum analyzer can tell you at what frequency there's high power. That should shed light, too, on how you should direct your effort.

One rule of thumb would be that devices that create a lot of noise seldom are bothered by it, so isolating them with a bypassed resistor won't hurt.

A small cap on the wiper of your POT might be a big help, too, BTW.

RE