Well, the colored objects are indeed unexploded images. You’ve got a bunch of reversed faces, which don’t seem to be the problem. No z-fighting (except as observed by @slbaumgartner) . No clipping.
Going all the way back to your first screen shot, I don’t see any of the triangular artifacts.
Maybe Wo3Dan is right about your video card. To confirm that, try going to Window > Preferences > OpenGL and turning off hardware acceleration. What happens?
-Gully