Looks like an unfortunate meeting with a lawn mower to me. No, coins do not leave the US mint looking like that.
Mark, as these quarters don't have letters and numbers on the edges, and as there's no error in the minting process that will put letters and numbers on the edges, that in itself says this is no error. The letters and numbers you're seeing on the edge are just damage, that's all.
Please do not hijack someone else's thread with a coin that has nothing to do with the original coin in question. I see you already created your own thread. That's the correct way of doing it.