My only question is why does this only happen on HD channels? The SD channels of the same programs are fine.
With no compression or equal compression, hd would require vastly greater bandwidth than sd, because of its far higher pixel count. Therefore the cable company compresses the hd channels heavily, resulting in the fast-motion artifacts you are seeing, while compressing sd (on sd digital channels) to a much lesser degree. And sd analog channels, by their nature, have no compression at all.
Also, for those who may be concerned about signal strength on their incoming cable, if you have your internet service provided via the same cable you can usually determine your incoming signal strength (as it exists at the cable modem) by interrogating the modem from a web browser program on your computer. My Scientific Atlanta cable modem is interrogated by entering http://192.168.100.1, which will cause it to return various status information including incoming signal strength. If that number doesn't work for you, Google the modem's make and model number and you'll be able to find how to do this for your particular model.
But I don't think the op's issue has anything to do with signal strength. The sensitivity to motion in the picture, and the fact that it only occurs on (multiple) hd channels, strongly suggest that it is due to compression applied by the cable company.
Regards,
-- Al