I’ve double checked all the normals, they’re fine, and all the transparency and alpha is unchecked in the materials and textures. I’m at a loss. Can anyone help me out? If no one has a quick solution I’ll post the .blend
Do you have any n-gons in those areas? Do you have that model rigged? Another way that things get displaced is if you have too many bones weighted to a vertex.
To me it seems the second image is rendered with transparency since hair seems to have transparent pixels.
If you are using dupligroups, armature etc make sure you disable alpha for the right mesh object. But I’m pretty sure that is the issue and it’s just a matter of getting the alpha settings right.