Thanks so much, everyone, for your opinions so far. @Root River Mint, I see the plastic bits from the PCGS slabs holding the coins in position, but the rim damage I am asking about is seperate. The 16 star one, in a PCGS MS(61) slab, which all the pictures are of except for one, seems to have a bit missing around 9 o'clock on the obverse. It seems the newer slab, which bears the D. L. Hansen name on the slab, actually hides the dinged/missing portion of the rim behind one of those three plastic bits. The older slab, from an older auction photo, reveals it.
I have seen both of these coins' written descriptions on auction sights, and am wondering why they don't even mention the rim issues. The auction descriptions obviously aim to "sell" the coins, but they often do concede or acknowledge the coin's biggest flaws (hairlines, muted luster, etc). The fact that auction houses don't even acknowledge these rim issues makes me especially curious what is going on with both of these (amazing) coins.