It's a 20k pot, but the resistance isn't that critical. Anything 10k-50k should be fine. I have noticed erratic behavior from the servo if you use the pot without the knob, and touch the metal with your bare hand. I think most of the odd behavior is due to capacitance in the buttons, which would get discharged if I tried to test it with my meter.
I tested the next batch of Arduinos in my winder rather than the testing jig, and found that if there was some odd behavior, pulling the Nano off and putting it back in (powered down and USB unplugged of course) would often fix it. If it still didn't straighten out, I rejected it. A few were doing things like restarting at random or not powering the laser.
I've also found that sometimes if you plug in the USB and try to connect while the main power is on, it won't connect. Make sure the power is off when you plug in the USB. Once it has connected to the computer, it is ok to turn the power back on.