Is there a way to suppress the vertical retrace when you shoot a TV or monitor with your DV cam? Those lines keep traveling up on the screen but some professional movies show a "smooth" TV screen when the scene takes place in a living room and the character watches TV.
If your camera allows it, try shooting with a slower shutter speed.
Usually in big budget films, special monitors are constructed that can be synced with the camera's shutter. Or, probably even more common these days, the scene is shot with a blank monitor and the image is composited in afterwards.
Look in your camera's settings for something named "clear scan" or something like it. It will slow the shutter to 1/60 of a second, or some facsimile. Also, if you really need the monitor showing, shoot an LDC monitor and then the monitor's refresh won't show up.
Or, as mentioned, you can usually rent from a film/video facility, a monitor that is designed for this sort of work.
Usually a shutter speed of 1/60th sec or a multiple (1/120th etc) works well since NTSC is showing 60 images (fields) per sec. If you're in PAL countries , try 1/50th or 1/100th if available on your cam.