In theory, there's the Fool's pass (ATG under the nose) that is pretty dangerous. But because everyone knows it's dangerous, I guess they take it easy on that pass. Indeed, letting your guard down while holding a razor to your skin is a fine way of acquiring red stripes on your face.

Personally, left of my chin is a spot where sometimes my razor gets stuck ATG and if I'm not careful, well... Same spot on the right side of my chin never has issues.