What's the source for the 1080p video? 1080p from YouTube is much different than 1080p from a Blu-ray disc. Also what are you using to play the video? Do you do any sort of gaming (or other high-load activity) and if so, does that have any similar symptoms?
Hard to say what's causing it unless you tell us exactly what the source material is, whether it's being played off your HDD or streamed, whether a software or hardware player is being used, etc. Could be any one of a number of things.
After further testing, it seems it's the files that are the problem. There's no problem with YouTube HD. There's no problem with playing BlueRay discs and ther'es no problem playing high end games. The files I'm having trouble with are .mov files that I downloaded from Footage Firm. I've downloaded both SD and HD files from them but only the HD files are giving me trouble.
I wonder if it's possible they got corrupted on the download as I have a weak internet connection with Hughes net satelite.
Someone else suggested using "integrated graphics". I don't know what that is.
Thanks to everyone for your replies and suggestions.
I still don't know how to determine if those .mov files are corrupt.