I suspect that the "mold" is mild corrosion of the brass case caused wither by the acidity of the cardboard ammo box or a bit of moisture from years gone by .... which appears bluish green most of the time.

Ammo for a 243 Win. is relatively moderately priced and easy to come by. Waht you have is probably still serviceable, bit I would not shoot this stuff simply out of an abundance of caution.

Check with your dad to see when the last time he thoroughly cleaned the rifle. If it has been a while I'd break it down and clean it throughly. Heck I'd probably do this anyway. If you are not familiar with breaking down this design, it is rather simple and good to know how to anyway. Now's the time to learn.

Consider yourself very fortunate to have come across an older BLR in 243 Win. These are sweet handling rifles. Not to mention the "heritage" of this being your Grandfather's and Father's hunting rifle.