Starring and messy edges when smoothing or using sub surf modifier I have a problem that when I apply a SubSurf modifier to my project, it has some starring and messy edges around the connection of my spheres. My goal is to have a string of "bubbles" which are smooth. I would also like to be able to rig them under one armature. The seams for UV unwrapping should be able to be placed where the spheres connect. I have used a Boolean modifier to merge the spheres. The problem I am having is that when I try to smooth out the spheres, starring occurs at the top and bottom of them. I have tried using loop cuts, the smooth option in the tools menu, and starting with a high-poly model, but none of that worked for me.

Here is an example of the starring: 



Here is how the spheres should connect (Please ignore the starring and high-poly count):




And here is a download to what I would like to end up smoothing out: http://www.mediafire.com/file/e6xeb5i74ii2t79/BugZHugSave3.blend1

If you have questions, please ask.
You should avoid Boolean as much as possible. Often it doesn't give a good topology.

If you want to keep your object:


Go in Edit mode, select all and press ctrl N to make Normals Consistent.
Press ctrl W > Remove Doubles to delete all the vertices that are very close to each others. Play with the parameters on the bottom of the Tools panel (T to display).
In Object mode, increase the View Subdivisions of your Subsurf modifier and press Smooth in the T panel > Tools > Shading. You could get something not too ugly.


But you should redo your object this way:


Create a sphere, rotate it, cut its top.
Duplicate this sphere and rotate it 180°.
Merge the two spheres with the Snap tool enabled (horizontal bottom menu of the 3D view), Type of element > Vertex, and press the Automatically merge vertices option.
Scale down one of the sphere, add an edge loop to correct the topology.