Hi David, This sounds like some sort of bug in the Finder. Can you try replacing the file? That is, create a blank file, rename it to match the MPEG, then drag it over the top of the MPEG. If the Finder allows this, are you then able to drag the replacement file to the Trash?
Perhaps you "should" also check your disk with Disk Utility (in the Utilities folder within the Applications folder). Open Disk Utility, select your hard drive, and choose Verify DIsk. (Give it some time to do its thing: attempting to do other things during the verification will cause them to pause until verification has finished.) James

