help with some render artifacts

[jp_li]

looking for some help to trouble shoot some artifacts I'm seeing.

#1  i can't get rid of these blocky shapes in the shadows and underlip of the surface.  two materials, back surface is a simple white diffuse material and the other is a plastic material.

#2  strange artifact on a flat surface, using a diffuse material.

Render settings:
Samples 20
ray bounces 6
anti aliasing 3
shadow 2
global illumination 1

[maymay]

Try turning on sharp shadows. I've had both of those problems. I'm not sure if it helps with the first problem, but it fixes the second one for me.