Well, I guess this is a half-baked fix, but at least it's a start.
The "waves" have indeed disappeared, so my Apple TV is at least watchable now. Unfortunately, it sends a 480p signal instead of 720p. So, apparently no HD for owners of older tv sets, only standard definition.
My television set doesn't display 720p (it displays 540p and 1080i), but it definitely supports 720p input (as stated in the tv's manual, and which I have tested with several upconverting DVD players in the past). It can accept 720p signal without problems and internally convert to 540p or 1080i.
Every other piece of video hardware I have ever tested on this tv has worked fine at all possible resolutions (except 1080p, of course), so I don't know why it is so difficult for Apple's engineers to get this working with the Apple TV. Hopefully, a future update will provide a definitive fix to this.