Bench power supply - Inconsistent voltage output
Yes, a bad pot could very well be the issue here.  I have a similar unit and I find that I got what I paid for which, unfortunately, is not very much.  My voltage display drifts over time so that if I set the output for 3.3V the display will drift up by 2-3 volts over time even though the output itself it pretty stable.
I've purchased a higher quality surplus (HP branded) unit that works much better.  You might consider the same thing or try replacing some parts to see if you can get better performance from yours.