I have a 2003-D Arkansas quarter. I was happy when I got it because I didnt have one. Then the next day I got another one. And after examining it closely, I see some kind of impression on it. I would say that the coin is in uncirculated condition because it has a bright luster and no scratches or finger prints but on the back, there is an impression, right above the diamond on the left side. It is situated below the 1 in 1836 and just a hair above the diamond. I looked on my other Arkansas quarters, and its not there, so I'm thinking it might be an error. The impressions are semi-circles, with the bottom half. There are 2 full semi-circles, and a part of a 3rd one. It ALMOST resembles the ridges on the side of a quarter, but I have no idea what it is. And sorry, I cannot give a pic, because my scanner is messed up, and not working.
In all likelyhood the marks you are asking about were caused by the edges of a quarter. They are called bag marks and occur when one coin drops onto another during the minting process. They are not errors.