I see it ocassionaly on my LG 4200 settop box, Also many of the supposed 1080 broadcast are actually analog shows redone to 1080 so that might be part of your problem too. The Niagra Falls show on PBS was horrinle becuase of that, History detectives, Secrets of the Dead, CSI...etc seem to be shot in native HD and look pretty darned nice.
Also if that set is a earlier HD unit more the a few years old it might be part of the problem too. The Cable box also may just plain have a bad scaler/encoder adding axtra crap so it's kinda hard to tell where your getting it from. Try here
http://www.avsforum.com/ and I bet if you give more details of your setup someone there can help you out.