Wow, extremely interesting what my problem has caused here:

New furniture, new shaders,... :-D

Ok, back to the problem: I finally solved it, thanks to Bills suggestion with the shadow-min-bias value.
Being not really familiar with Poser my fault was the mesh I imported.
I modelled the cupboard in C4D and in a silly attempt to reduce poly-counts I decided to make the blinds and the floors of the drawers as zero-thickness planes, just with "folded" edges, if you know what I mean.

Like this ____/  intstead of a closed form.

In C4D this worked fine, but in Poser this did not cast a shadow as I wished.

By the way: My units are in mm, but shadow min bias value did not change when I changed to inch.

@RobynsVeil: Diffuse Value was 1, now I changed to 0,9 which is way better, thanks for that!

To the final result shown above:

Left is with IDL using BagginBills EnvSphere with an interior HDR picture, one light from left top, white at 80% intensity. shadows raytraced at strenght 1.0, blur 2.0 and min bias 0.05

Right one is without IDL, envsphere deleted, 2 more lights with same settings but fill-light from left at 60% intensity, top-left-light and back-light at 100%

Well I really have to say I start to like the firefly renderer with IDL :-)

 A lot a thanks to all who helped, I really learned a lot!!!