I've heard that they can rival scalpels.
The reason obsidian is so sharp is because it breaks on the molecular level. Tiny flakes have been used in eye surgery because even the best scalpel cannot be sharpened that fine. They are very delicate. Obsidian made into arrowheads or knifes cannot have that delicate of edge.
I had no idea it formed edges that sharp. But then, it is a form of glass, and when glass breaks, it sometimes forms into tiny hairs that slice through the thickest skin (like my heels - I've stepped on a few thanks to my cats and dogs and kids breaking glasses). I've read all kinds of interesting things about obsidian now, including this:
For those with the patience and persistence to learn, beautiful stone arrowheads can be chipped out of flint, chert, agate, obsidian (volcanic glass), and even man-made glass.
From this site:
http://www.midwestlandcompany.com/newsletter/The article is about "The Return of Primitive Archery". Seems topical.
It seems that some people do make obsidian arrowheads, although I can understand the worry about them being fragile. A bad hit (or miss) could shatter the head, I'm sure.