You just have to practice and learn how to crop We juat see a fuzzy image Which looks kinda like mechanical doubling but i don't about these coins and cataloged errors.
Cool Barber. Looks like a shelf on the 2 so likely machine doubling. Take a pic looking straight down at the coin and not at an angle.
Notice how the bottom of the 2 appears to be significantly thinner than the rest of the digits. Looks like it was took a hit and was damaged You really need to take the pic looking straight down on the coin. It would be a lot easier to see what you have.
The mark looks like a straight line in all your pics. Since it doesn't follow the contour of the the 2, it can't be a doubled die or Repunched digit
After eliminating the impossible, whatever is left, however improbable, is the solution. By the way, a scratch or dent over a 117 year period isn’t very unlikely.
I agree a scratch or dent isn't unlikely but if you would see this coin in person you would agree it can't be just a scratch. Perhaps a knife cut as @Collecting Nut suggested, but I am not to convinced I would like to look in to it more.
You’re asking the wrong question. You want to ask “How could this occur at the mint?” There are multitudes of ways for a coin to pick up damage in the real world, but during the minting process, the number of ways an error can occur is limited and can be explained. So focus on how this could occur at the mint and don’t get hung up on “I can’t explain how this could be PMD, so it must be an error” I can't come up with an explanation of how it could occur at the mint. It can't be a doubled die or RPD because the line does not follow the any contour of the digit. A strike through would be extremely unlikely because the line doesn't travel beyond the 2. Any debris would have to fit perfectly in the recessed 2 on the die. Filled die? Doesn't look raised and it is unlikely it would form a straight line. Since I can't explain how the mint could make this, nor have others been able to offer a plausible explanation, it must be PMD There is always room for additional research, especially since you have the coin in hand, but remember, you need some compelling information to show it's a mint error
Obviously Some descendant of captain flint checked the authenticity (using the tooth check method) when someone boarded a ship OR Uncle Buck had to check the spark plug gap on his model T in route to California. Looks like post mint damage though.