Here's an update my my three problems with shooting movies with the D4:
1) With respect to the intermittant severe stuttering, I noticed that there is an anti-flicker setting in the menu. I am skeptical that it will solve the problem that I observed, but will certainly give it a try.
2) Buried in the D4 manual (p.64) is a poorly labelled grid that reveals that ISO changes can only be made in movie live view when the camera is set to Manual Mode. That strikes me as a poor design decision, but I verified that it works.
3) I've done more film clipping, and all frames are 1920 x 1080 pixels, which is adequate for 4 x 6 prints but no larger. By shooting video with the D4, the photographer loses the chance for high quality images of the same scene. That makes for tough decisions in once-in-a-lifetime situations!