Settings in Picture 4

First problem seems to be greatly reduced, but it is not quite gone.

And the second problem remains. It actually reminds me of something, which often happened when using AO. SO i attacked the texture first of all. Replaced the current texture, which is by Ajax, with a simple white. No change

Then I upped the shadow samples to 30 and reduced the bias to 0.1 for my light. No change

Then I tried to switch off smooth polygons, just in case. No change.

Finally I thought that the spots might be smaller at a larger scale. So I parented the whole show to the IDL-dome and resized that to 10000. No change.

I am not sure what to do now.

Would anyone have had the same problems and some brilliant solution?