The staples are rusty because they probably are not galvanized like roofing nails are. If the shingles are being nailed along the tar mark or above, this is correct. When the next row is put on, the nails will penetrate the the top of the previous row. Is the mildew on the inside of the attic? If not,how did you see under the shingles and tar paper? If you're seeing water marks on the sheathing,have it repaired. Remember,we are not there to see your problem. The best way to handle this is to get another opinion from 2nd contractor. Ron J.