Random Artifacts appear when I try to apply texture to part of mesh

I’m working on a character. Modeled, looks great, try to add a material to part of the mesh and then it goes crazy. I can see the random planes that stick out are the color I added, but they have nothing to do with the model. Also I sometimes see infinite vertices surround my model but can’t select them, or get rid of them and think the two problems are connected.

I tried adding a texture to one side of a new cube and the same thing happened only not as severely. I tried resetting to factory defaults, just in case I done something, and that didn’t help.

The longer it sits the more artifacts just keep increasing.

screen shot 4

If I did it right here’s the file.

Snapper Bottom Shell 1aT.blend (2.1 MB)