Explanation for super-sensitive loose contact inside potentiometer?
Here is what the inside of a different type of pot looks like:



Your pot will have similar construction inside to this one, though it will be hidden by the molding. There is a metal part that connects to the circuit board. In the photo it's held by a rivet or similar crimped construction to the substrate, which has a silver conductive printed portion overlapping the resistive element. 

If the rivet on the 'low' (CCW) side becomes loose, the exact symptoms you describe will happen. Same if the substrate is cracked. Your type of pot may be slightly different- perhaps the lead is embedded in a conductive epoxy rather than a rivet, but bottom line is that there is a transition from the pin to the substrate to the element and somewhere it is intermittent. 

If you replace the pot, the problem should go away. 

But first, check that you have not missed a lifted pad on the PCB which is more likely on a single-sided PCB. A crack between the pad and the trace can be difficult to see- wiggling the pot and looking at the pad with a magnifier in good light may help. Be sure to clean any flux off of it first with proper flux remover. 

Components such as pots are frequent sources of trouble, either from breakage or from damaged PCB conductors because they're connected to the outside world, and users can be rough by times.