A new hard disk should have zero bad sectors on it. An older drive may "grow" a bad sector or two now and again, however in many cases this is a harbinger of impending disaster with the disk. Take it as the warning sign it is.
In my opinion it would be foolish to assign as extra storage, a disk which you now know is becoming potentially unreliable. Don't be a cheapskate. With the price of hard drives as they are these days, re-using it in your son's computer is a false economy.
