Strange behavior from variable-gain amplifier
I think the clue is that you see noise on pin 5.  I suspect C4 is open and that a 1 k&Omega; resistive impedance is not sufficient to hold the pin at a steady level.  As a result, the input is oscillating or doing other strange stuff, which results in a different volume level for the same average DC level.

Hold a 10 &micro;F or so cap between pin 5 and ground and see what that does.  If there is still noise on the pin, then read the datasheet carefully about what filtering and possibly minimum capacitance is supposed to be on that pin.  If everything works as expected with the 10 &micro;F cap there, then either just go with that or check the connections to the 1 &micro;F cap.  You might find a bad solder joint or ground connection.