Because you don't need dimensional anything to tell threaded from non-threaded to start with.
I do think that this is a valid question for us to ask as the OP provides little information for us to work with. Certainly we’ve seen many posts where the OP comes here looking for permission to discipline an operator or inspector for ‘screwing’ up (pun intended) and they withhold (deliberately or not) critical information that would get us and them at the true cause…and most of us have experienced this very thing in our own work.
It would be a valid question for the Quality Manager to ask if they haven’t yet done so. The missed visuals could be just the tip of the iceberg of what is wrong here. The OP has stated that they are a new QM and they don’t even know where to start to fix the issue…The OP really does need to understand the system they are working in. If the machinist and the inspectors all missed the visual then it makes sense to ask about the other dimensions. There should be several dimensions to check in a first article for a screw. If not, why not? If so, are they correct? If the obvious visual was missed were the dimensions requiring measurement also missed? (That would be a BIG hole in the system) And usually the threaded part would be a dimension on the print…not simply a visual check that some undefined area is not threaded.
Too frequently a seemingly simple event of missing a visual criteria is just a symptom of a greater problem. An important part of a Quality manager or engineer’s job is to be able to think critically and deeply about the system. As a profession we suffer from shallow ‘cut and paste’ thinking and mere compliance to some standard that isn’t even read, let alone understood. If it is unacceptable for the inspectors to have "don't give a "S"-itis", then it is doubly unacceptable for the the QM to have "don't give a "S"-itis"…