I'm not sure what you are referring to. We have two video players and a wii hooked up to one television, and a pS2 and PS3 connected to a second TV, and a PS3, PS2, and a Xbox 360 connected to a third television. The fourth television has a NES, SNES, SEGA, VCR, and DVD player connected. The fourth television has been connected like that for over ten years and it suffered no damage. The other three, all HD flat screens have been connected to multiple items for over five years and have shown no signs of wear.
I wonder if there is a bad/crossed connection somewhere. The only warning I am aware of is Pixel burn, which happens if you leave a game on without a screen saver for a very long time. Most new games goes into saver mode if you leave it for more than ten minutes.
When we first set up our large HD we had cable bleeding through the video movies; however, once it was reconnected (properly this time) the bleeding stopped.