I believe that the turning point you are referring to is the discussion of Joe's excellent health over the years.  Kate states that Joe hasn't been sick for fifteen years.  However, Joe claims that he didn't go to work the day that Steve shipped the faulty parts because he had pneumonia.  He and Kate try to cover this up, but it is apparent to George that there is something fishy in the story.  Up until this point, there was the possibility that the Kellers were going to win George over to them (as they had won Ann), but this moment turns the play towards its ultimate tragic end.  George is unable to let go of this inconsistency, adding to his theory about his father being too weak of a man to order the shipment without Joe's approval.  This then pushes the play to the revealing of the letter from Larry and the truth finally being acknowledged (Joe's culpability in the shipping of the parts and Larry's death).