Any tips/secrets to filming a picture on a television set; Or a computer screen with a JVC GY HD 200?

If you are shooting 24P switch the shutter into variable mode and then dial in a multiple of 1/59.94 for NTSC tv screens. Computer screens can have many different refresh rates so it is easiest to check the display Hz and just dial it in on the camera. You will see the effects of the shutter as you make the fine variable adjustments. The goal will be to eliminate any rolling bars or flicker.

And remember the light source is close to daylight colour temperatures. (ie. NOT 3200k)

Any panning or zooming is likely to cause scan lines to appear briefly, ruining the effect so the effect is BEST pulled off in a locked off shot.

Sometimes it works/helps to set the refresh rate on the computer monitor to 60hz.