This is already a pretty wordy discussion, but anyway...
Watch for reflections in the screen.
If you can see a reflection with the display off, there will
be some overlaid image effects with the display on.
Careful control of surrounding light levels can lower the
effect while still allowing photography of the rest of the machine.
The video* signal is strobing at something like 30-80 hz.
The camera's shutter speed should be slower than at least 1
frame of the screen. I use 1/20th second for noncritical work.
Those are the big 2 factors. Flash should be off for those reasons.
If you have autofocus=off, autoexposure=off controls, use them too.
* flames off plz
John A.