If this is "Production 101," I apologize, but this is what I think.
Technically nothing is ever formed exactly right except by chance. The job for a factory, machine shop, or craftsman is to get it so close to right (tight enough tolerance) that the remaining error does not compromise performance, fit, function, feel, durability, or appearance. If you were to look at a "smooth" surface under an electron microscope, you'd see something that looks like the Rocky Mountains.
Mirrors do not have specs that say "perfect." They say things like "allowable tolerance 0.000002 inches" or some such number.
I'd start by looking in McMaster-Carr for precision measuring tools, then perhaps (walking up the price ladder) to Edmund Optics and Scientific for how optical surfaces are evaluated. At some point looking at tools priced from $300 to $30,000 a pop you'll think "how good does it really need to be, and why is what we normally do not good enough this time?" and then you've arrived at the right question.
I assume in his shop there are some digital mikes or surface gauges stored in fitted wooden boxes in a locked cabinet along with some surface plates, that are used for tasks like this. I can't imagine a good shop foreman accepting a job that he couldn't accomplish with reasonable margin. Over-working the smoothness can eat up your profits.