The latter sounds like a possibility. The signal quality varies on the dodgy channels but stays static on the ok channels. I have fiddled with the connections and if I waggle it then it makes it worse. The fitters were also monkeys (they drilled through a phone cable and were completely flummoxed by an adsl faceplate, even after I gave the guy the wiring diagram for it! )So it'll be a problem with your hardware.
It sounds simply like there is not enough signal there to generate a stable picture which could be caused by a damaged cable or LNB when trying to access the frequencies used by the affected channels.