Updating with what I had to do to "fix" the problem.
I called Apple support and they walked me through what they thought would fix the problem. In particular, they had me do some sort of hardware reset. After this reset, I would no longer get a login prompt after rebooting;the MacBook would get stuck on a gray patterned screen. The Apple support person was unable to get me past this new problem, so she had me go to an Apple Genius Bar, which was conveniently a block away.
The support person did a non-destructive reload of Lion. Did nothing. I had a good Time Machine backup from immediately before the upgrade to Lion, so the support person did a destructive install of Lion.
I went back to my office the next day and ended up doing three reinstalls of Lion. The first time, I restored all my home directory files, settings and applications from the Time Machine backup. Both the desktop switching lock-ups and not getting a new login screen occurred. I did a destructive reinstall of Lion and only restored settings and my home directory. The problems reoccurred. Finally, I did another destructive reinstall, restored only my home directory and reinstalled the applications I absolutely needed. The problem has not reoccurred.
So anyway, I fixed the problem on my MacBook Pro after about a day of repeatedly reinstalling Lion and restoring files/software. I've been cautious to only about reinstalling applications, fearing that one of the applications I had installed before Lion had tickled the behavior.