on a shelf. I turned it over a few times. Would it be safe to mount and ride on?
I wouldn't hesitate to mount a one or two year old tire as long as there was nothing obviously wrong with it. A number I have seen mentioned many times for the maximum safe age of a tire is five years. I don't know how accurate that is but after a certain period of time a tire will start to "dry out" and will have less traction especially when wet.
Look for the date code inside an oval. Two-digit week followed by two-digit year, e.g., 1411 means that the tire was manufactured in week 14 of year 2011.