Due to the difference of the color/toning of the affected on the 1968 Quarter, IMHO it is post mint damage and believe that the affected area on the 2001 Quarter is also damage. The 1965 Quarter either went through a dryer or was ground down to accommodate setting it into a bezel but I am leaning more towards the latter.
Looks to me that the 1968 quarter has been ground down on about 2/3's of the coin. It doesn't look perfectly round anymore. The edge by the date looks good, but the rest of the edge has been worn away. Wait a sec.....on second look, it looks like you cropped the photo that cuts off some of the edge. In that case, it think it was just a quarter that got caught in a machine and was damaged that way. Definitely PMD.