Thank you. I have indeed not closed the eye piece and it looks like that was the problem. However, Darrel Young mentioned in his book on the D800 that it does not make a difference (p482), so that's why I did not bother.
In addition, Darrel Young says that LV mode is for "extreme focusing accuracy", especially for close ups. I now you asked for pictures (computer still under repair), but the live view really does not want to focus on a foreground subject like a pink rose against a green background. I still have to first show it the way, by non-LV auto focus and only then it manages to find the very prominent subject.