Using AF with a Nikon in live view, gives the camera controls over to contrast detection, which as the subject moves, or lighting shifts will cause the lens to rack back and forth.
The difference between phase detection (DV cams) and contrast auto detection on HD enables DSLRs, is perhaps not something the director was aware of.
One (best practice) should never use auto when shooting video with a Nikon, or Canon generally.
The lens also, does not have a fixed aperture f/3.5-4.5, which causes issues with exposure during record when the lens is racked, or if someone with a dark or light shirt walks through the frame. A nightmare to fix in post BTW.
I shoot my Nikon video with manual, setting the focus in live view then switching from AF on the lens to M to lock the shot.
One can also set the AF button to lock on camera.
If one has the latitude to use f/8, and exposures do not suffer, then the shoot should be adequate if on a tripod with minimal pan and tilt.
If hand held, even more so.
Some DP’s shoot at f/5.6 and get good results but I have footage where we are shooting wide open, so that will vary.
Imagine shooting everything with this type of technique and assuming a still or graphic will be inserted to cover the changes when you do refocus or, shoot two DSLR cameras so you can jump cut.
In this case of course, it seems to be too late.
HTHs
Rob Manning