After reading this thread pretty carefully and trying everything I could think of, I finally called Apple. It took awhile to get to Jason, the second-level specialist, who was very, very polite and accommodating, but after going through a lengthy litany of procedures, and finally trying a video which performed perfectly (making me a little nervous) before freezing after nine minutes, he agreed to replace the unit. My provisional conclusion is that some small subset of iPads are afflicted with this problem, and that Apple as an entity is either not yet aware of it or not willing to acknowledge it. But their service people are so astonishingly conscientious that, as frustrated as I am, I am still proud to be an Apple fanatic.
I have lots of other Apple products, including an original "1984" unit I am keeping, because someday it will make me rich. I think this iPad thing, which I bought even though I dismissed it as nothing more than a Maxi-Pad (which it is), is still an incredible breakthrough. Like the little girl in Steve Job's recent presentation of the new operating system, who hugs the machine as if it were a Teddy Bear, I am very, very fond of this device, and I grudgingly forgive Apple for breaching their normal high standards of quality control.
