Hi astracat,
Moir patterning......now there's a term you don't hear much nowadays. There are a myriad of hopeful cures out there, like toggling the Noise Reduction settings on your TV or lowering the output resolution of your cable/sat decoder. My question firstly is : Does the TV use a ChiMei (CMO) display panel? These are reportedly notorious for it.
Lately, I've found that Panels which have a plastic backing i.e no metal to provide shielding, can play havoc with the eeprom data. This may prove to be pure twaddle, but if the plastic backing is the case with your TV, I can furnish you with simple steps to cure it. May involve a visit to Oil Drum Lane though.
Bruce