There are any number of things. Since you say 'stamp' and 'over and over', I'm guessing you don't mean one light kick. Other than possibly death, fractured bones (cheekbones are relatively easy to fracture) and brain bleeds/trauma are probably the most serious. As to what you'd observe, lots of blood (a punch can tear the delicate skin on your face, with it being so close to bone, so a stamp would tear a lot), loss of consciousness, fast swelling and heavy bruising. Even if they didn't pass out, they'd probably be very woozy afterwards and wouldn't be getting up anytime soon.