Strange Mesh Artifacts

So I have this mesh:http://i.imgur.com/tws4E6v.png Great! I might try to turn it into a bomb, with a little more smoothing. The problem is, it does this: http://i.imgur.com/UemTu2Y.pngAnd I have no idea how to fix the artifacts towards the top of the mesh.

Inconsistent face normals. You can display normals from the properties panel under Mesh Display settings in edit mode
In this order:
Remove any faces inside the mesh
Remove any doubles vertices - select all vertices and W / remove doubles
Recalculate normals - select all vertices and Ctrl+N
Flip any faces still pointing the wrong way - select face and W / flip normal

Brilliant, my friend! You are a true blender hero! However, despite the fact that I have a 3D vector calculus class under my belt, I can’t figure out the contextual use of face normals are. So, in other words: what benifit does keeping track of face normals provide in this case? and: How does blender choose which way the normal vectors go?

That is just for face normals?

In other words: what ARE vertex and face normals?

Simplified, view it as being the direct the face is pointing. If you have a cube you want all the faces pointing outwards from the centre of the cube. If you have one face pointing inwards that’s were you get these shading errors on the boundary between the inwards and outwards facing faces

Normals are very important in meshes, even though they do not really contribute to the shape itself. They are mainly used in the shading of a mesh, but they also define what is “inside” and what is “outside” – which might be very important with some tools, like e.g. the Boolean modifier.Technically, in a 3D space, only faces have normals (the normal of a surface at any point is the vector perpendicular to the plane which is tangential to the surface at that point). However, it is sometime useful to have normals for vertices, and even edges – the later being interpolated from their two vertex ones.There are two cases for vertex normals:

  • If the vertex pertains to one or more faces, its normal is the interpolated value of all the normals of these faces.
  • If the vertex does not pertain to any face, its normal is aligned with the line from the object’s center passing through this vertex.