If I am correct it is an entirely different effect in your second pic.
Subsurf problem: Easy, don’t use triangles when working with subsurfing. You can use “degenerated” triangles where two points are at the same position, so it looks like a triangle but is a quad. Example. Imagine a mesh circle. If you want to fill it, you can extrude it and scale the extrusion to zero. If you now remove the doubles, you have a set of triangles around the center. This will be ugly when subsurfing. When you just don’t remove doubles, the geometry looks the same but consists of quads and works with subsurf.
Problem two: Don’t know exactly, looks like a low color resolution. Don’t know how to avoid it yet. I noticed it too, but for my usage it always was negliable (only seen when zooming extremly, not visible with structured textures, not visible with AO).