To my knowledge there has never been a case of a person seriously injuring himself while shaving. Superficial cuts are no more common than with any other razor blade, either. The two most dangerous times are when you first start out and once you think you've "mastered" it and lose respect for your blade. When you first start out, you'll probably get a few nicks, but nothing to write home about. Irritation and red spots, probably due to a combination of poor technique and trying to use a blade you honed ineffectively yourself (practice makes perfect).
Then you'll probably get to the stage where you're delighted with your uncanny prowess with your straight razor and start getting cavalier with it. Damn, I'm good, swish, swish.... flick, swish,flourish, OOOOHHHH DAMN that's gonna leave a mark. :(.