Just for your info on this. Vertical lines of interference usually indicate HIGH frequency noise of some kind. Horizontal bands that creep up or down on the screen usually indicate LOW frequency noise such as 60 or 120 cycle hum due to ground loops or poor power supply filtering in some component along the cable system or a VCR or TV. In the case of high frequency noise, this can be a poor ground picking up digital noise from almost any component these days as they almost all have microprocessors in them. By replacing the splitters, the connectors on the RF cables, or using newer, better quality RF cables, you can help eliminate the interference you are seeing. Also, it only shows up on certain channels because the noise is "beating" with the channel frequency much the same as whistles can be heard on AM radio when another frequency that is a harmonic of the station is being picked up at the same time.
Bottom line: make sure all the connectors are really clean, use good quality RF cables, splitters, and amplifiers and try to keep all of the RF stuff away from power lines and the power supplies of things like VCRs and computers. Periodically clean those connectors with a good quality contact cleaner.
Joel N.