Frank,
API 570 Clause 5.11 Inspection of Flanged Joints doesn't address the issue of reusing stud bolts. Is there any better reference?
However, just for comparison, every time you open a flanged joint, you are reusing the old stud bolts (unless you have reasons to replace them). Conversely, I would say that the bolts used in a similar environment and not subject to advanced corrosion can be re-used for continuing service. I assume the type and size are identical to the calculated/designed ones. This judgement doesn't include the unknown source of bolts and nuts.
I don't know any standard allowing you to inspect and test the bolts before installing them in operation, but many NDE companies offer Dye Penetrant and Magnetic Particle testing for fine discontinuities on the studs surface.
It all comes down to the costs involved, sometimes the inspection costs could overrun the new bolts cost. One thing for sure, the cost of new bolts will always be lower than the cost of joint failure and the subsequent disaster caused by bolts failure.