The only possible problems that come to my mind would be either HyperNURBs Weighting gone awry or that some of your vertices are not connected. I have a suspicion it may be the latter based on the funky Phong shading around the problematic vertices even pre-smoothing.
Easy way to check for the first if you've applied any HyperNURBs weighting is to select the tag on the object.
Easiest way to fix the latter would be to:
1) Select the object and run Functions > Optimize with the last check box selected and a Tolerance of 0. This will weld any vertices that occupy the same space together.
2) Put a Connect object in the hierarchy as a child of the HyperNURBs and a parent of your model. Make sure that Weld is enabled on the Connect object and set your Tolerance low (0 should work).
When you use Extrude NURBs (as well as many of the primitives) the individual faces are not connected to one another, the vertices along the edges just occupy the same space.
Darby Edelen