Offspring:
The model number is stamped on the frame in the cut out for the cylinder yoke (crane). It will say Model 10, Model 10-1, Model 10-2, etc. The '-x' refers to an engineering change. If there is no -x after the Model number then you have a tapered barrel model 10, these were produced from 1957 to 1961. The -1 was introduced in 1959 with the heavy barrel. The -2 in 1961 changed the ejector rod thread from right hand to left hand. The -3 made the same change on the heavy barrel version and changed the front sight width. In 1962 the -4 deleted the screw in front of the trigger guard on the tapered barrel, the -5 changed the front sight width on the standard barrel and the -6 deleted the frame screw in front of the trigger guard on the heavy barrel version. There were no more engineering changes until 1977 with the -7& -8 variants. By 2002 S&W were up to -14 with the internal trigger lock.
IIRC S&W sold Taurus the original machinery used in Brazil to produce their revolvers, which may be the basis of the story you are thinking off. You will find many threads on this and other forums where people moan about the quality of S&Ws going downhill, but the fact is that S&W quality is fairly good these days, the use of metal injection molded parts means that there is a set standard of quality, you won't get a work of art lovingly put together by a craftsman, but nor will you get a gun hand fitted by someone with a hangover whose wife just cheated on him.
Guns with problems do still leave the factory, but I've yet to see the inconsistency that I've noted with some guns from the seventies or early eighties. For what it's worth, your revolver dates to a period when S&W quality control and craftsmanship is considered by many to have been at it's highest.