UPDATED-4/3/18-------I never really noticed how scratched my slabs were...............

Certainly. There are probably dozens of threads on plastic polish. It works very well on PCGS slabs.

Manual focus and a good macro lens will shoot past very minor scratches. Auto focus tends to zero-in on them, not the coin (which appears to be the case with the OP coin).
Lance.

Cool coin!

@ErrorsOnCoins said:
I recently got in the worst scratched (PCGS) slab that I have ever seen.

I decided to try something new.

Took out the new Dremel with polishing compound and went at it. Was working petty good until I up the speed and barely melted the plastic. Oh, Chit. now what.

Then I remember a thread here on using sandpaper on a slab and said wtf, why not try that.

So, I sanded a bit with 400 wet dry sandpaper and said wow, I really messed this one up.

Then I sanded it with1500 wet dry and it still looked effed up.

So I then took back out the Dremel with a ton of polishing compound and used the tool at low speed. Back and forth in different directions.

Came out like glass

Now you can poke a Q-tip through it.

@ErrorsOnCoins said:
I recently got in the worst scratched (PCGS) slab that I have ever seen.

Came out like glass

Thank you to whoever wrote the tip here years ago.

I think that was @bolivarshagnasty. He had great images to go along with the story. I remember he started by grinding the slab under his shoe, on concrete. It was painful to watch but the restoration was incredible.

A couple of years ago I picked up some "Zona 37-948 3M Wet/Dry Polishing Paper, 8-1/2-Inch X 11-Inch, Assortment Pack One Each 1, 2, 3, 9, 15, and 30 Micron" from here:
https://amazon.com/gp/product/B001BHGC7G/ref=oh_aui_search_detailpage?ie=UTF8&psc=1

This stuff is perfect for the job when scratches are too deep for Meguiar's PlastX polish. It's a little unnerving when you start with the grittiest paper and can no longer see the coin...just grey, opaque plastic. But the follow-up sanding (wet or dry) with the finer grit papers gets fabulous results.
Lance.

@disappointingcoins

For light scratches you want more of a transparent filler/polish, @1630Boston mentions one.

You have to be exceedingly careful using any tool that is electric. If any heat is created (even in a small spot the plastic will melt.
On a severely scratched PCGS slab 400 grit, 1000 grit, 2000 grit then PlastX.
NGC slabs have a far greater area to polish but the same process works.

Light scratches, just try PlastX.