(This is what I sent to the iTunes support team as part of my ongoing conversation with them)
I spent last night restoring my iPad to its factory defaults and then restoring it from a backup. As a result my iPad no longer shows the 2000 empty playlists and appears to be in sync with my iCloud songs. So that problem is solved -- though there's still no clue as to root cause.
However, now the iPad will not reliably play back the music. For example, I chose the first song in my newly-created "Christmas Music" playlist (not a Smart list), which the iPad started playing for a few seconds before stopping, rapidly trying to play each of the next 5 songs, skipping one of them. Then the Music app crashed.
On restarting the app, none of the songs will play. I've tried the wireless network as well as the 3G network, both of which have very strong signals. Clicking the iCloud icon temporarily begins the download process, but then stops. All of the other internet services on my iPad are fine.
On my iPhone4, the behavior is similar: I can play some songs in the playlist, but the iPhone often decides to skip the song I chose and play the next one in the list. Songs that play on the iPad don't play on the iPhone and vice versa. And the Music app just keeps skipping down rapidly to the next track, without even trying to play the songs.
I've tried playing songs from the "Songs" tab in Music and the result is even worse: the iPad can play one or two songs, but when I click to another song, it begins to download the song, then skips to the next song in the list, then freezes. The behavior is the same on my iPhone4.
This is very, very frustrating. At this point I'm getting to the end of my rope troubleshooting a product that was clearly released before it was ready.