The OED gives the following definitions:
a. A person appointed to examine or inspect something, either on a special occasion or permanently; in later use esp. an inspector or examiner of goods supplied by contract; †spec. in Law, one appointed by a court to inspect a place, property, etc., and report upon it.
b. An overseer, manager, or superintendent of a coal-mine or colliery.
Based on the context – the individual was a woman, and it was the 1950s – I think the first definition is most likely the one that applies in your case.
Here is a job advertisement from the Birmingham Evening Despatch on 25 May 1944:
You will note that this is an advertisement from the Hercules Cycle and Motor Company in Birmingham seeking female viewers (inspectors).
Another advertisement, from the Birmingham Daily Post, 24 Nov 1939, gives an idea of the technical skills one employed in this position may be required to have:
A search of other newspapers from the 1940s and 1950s will return many similar advertisements in a variety of different industries. The above examples may be war-related employment; the Second World War may have been a reason why more women became employed in this type of role. Other job advertisements were looking separately for inspectors and viewers, suggesting that viewers were in some factories subordinate to "Inspectors". There are many advertisements looking for male inspectors or viewers as well. The nature of the occupation of viewer no doubt varied greatly depending on the industry and employer, but it was probably quite skilled and technical work.