Well, yes. Tossing lower 4 bits of 10 total means clearly that the source signal is too bad to be useful. If Robert insist on using those pots, then based on the fact that the wiper moves slowly, he should have a really big time constant on the R-C network to compensate for the "noise". And then he should also add buffers with such high Pot and R-C values. All these add extra cost. Better chose a better pot and done with it.

Ioannis