Is the face a seperate shape than the hair? It should be - create one shape for the face, another shape for the hair on top of it, and maybe a third shape for the hair behind it.
The most likely explanation is that you have got one or more points on top of each other. I'm afraid the only solution (if you want to keep this vector shape) is to nudge each and every point with your mouse to check. It's happened to me a few times...
You can't have everything. Where would you put it?