1866 Shield Nickel W Details - Do They Matter?

Sure it lowers the value. When you compare it to one with the same grade without the scratches which is probably at VF30 or maybe XF40 which would you prefer? Don't be too discouraged. Learn the lesson of using a magnifying glass and studying a coin before you hand over the cash.
Possibly this nickel was priced lower than others the dealer had to offer and that is what drew you to it. It does have a lot of remaining detail but there are also rim gouges and I see the word "WE" in the motto is also missing.
That might be from the die being filled with grease and metal particles and it doesn't look too bad. I don't see where it was removed by tampering.
Don't despair, your nickel is still better than average of what you'll find with the amount of details yours does have.
It does have some issues but it isn't an ugly coin by a long shot.
I would not be ashamed of it.
If it were professionally graded, it would probably say scratched and or damaged on the holder with a grade of XF40 details.
I personally would value it at VG10 to F12 net with the issues and price it accordingly.
Lesson to learn. Take a magnifying glass to the coin shop next time and ask to look at a coin before you buy.
Welcome to the forum!

Thanks for the encouragement. Hopefully, the $60 I spent was not too much.

Also don't forget to check the 3rd side of the coin - the edge! Looks like a lot of rim bumps on your nickel, at wholesale pricing this nets a coin 3 grades lower in value when considered with the scratches IMO. I bought a lot of coins like this in my early days, but I soon learned, as I upgraded my collections, just how hard problem coins are to sell. Most of my early mistakes I gave away to younger collectors at my local coin club in exchange for their doing club projects (writing papers on a coin or numismatic subject - giving a talk, etc). now with several decades of collecting and dealing under my belt, I always try to buy the best I can afford in problem free coins, makes a trade towards an upgrade piece a lot eaisier.