Weird model display

That looks really odd. I am not even sure if it's Z fighting.

Try installing the latest video drivers for your card.

Looks like the memory on the video card is failing.

A driver update indeed did help. I should have tried that before posting - sorry. And thanks for the hint!

Still a doubt remains since I am sure that it did work on that machine before. Maybe I was using an older jME version there before my last test.