Now just think that those nano-scopic circuits have tons of errors when being developed and they need to be fixed before they can be sold. The manufacturing obviously can't work right out of the gate. In what industry does that happen?

So, there are electrical engineers, chemists, physicists and materials scientists out there who have to look at all of the information from all of tests done in all sorts of departments. They wade through petabytes of data from the manufacturing tools in all of the research factories and do all sorts of other stuff to figure out which circuits work and which don't and why. Any and all information they can use will be collected and investigated by someone, often with a PhD in the subject.

Then other people have to figure out how to dig into the processors so they can try to visually inspect those circuits or electrically test them or otherwise find evidence that these hypotheses are right or wrong. You can't do applied science without reliable data. These people who do the verification work do it with all sorts of expensive electron microscopes and very creative materials analysis techniques, skills that can take years to master. There are also researchers constantly trying to figure out ways to create new testing techniques because as things get smaller they become more difficult to investigate. Time is money so any way to speed things up is looked into.

And then, only when the company is certain that their army of engineers can interpret their mountains data correctly enough to reliably know the cause of a defect can they start fixing stuff. So they will make some process changes here and there and then.... other stuff doesn't work, when it did before, and the teams of people start again trying to see if the defects are similar to the last ones or completely new. Slowly but surely they fix as many critical defects as they can and eventually make a working product. It is an unbelievably painstaking process and people make whole careers out doing failure analysis on these computer chips and they can get paid handsomely for it.

You can get a taste of it if you sign up for a low level semi-conductor fabrication class at your local university. Most large schools have clean rooms and rudimentary development labs where they can make and analysis processes slightly older than what was pictured in this link. The problem solving aspect of all of this gives a new appreciation for how impressive all of this technological progress is, considering they put out new products multiple times a year!

Source: I'm a small link in the long chain of people who do this every day.