Touching Pin Causing PCB to work
What voltage do you measure on pin 6?  You should see about 7.5V.  If you don't then I agree that it seems peculiar.

If pin 6 was open it would give those symptoms.  The LM358 has PNP inputs so when open they will float close to the positive rail.  They only have ~20nA bias current so the 10megohm scope probe will drag it down to ground and lower than pin 5 so giving your high output.

It seems unlikely though that there would be multiple boards with the same bad solder joint.