Although the problem wasn't widely reported, I did find a few threads on the Apple support boards reporting similar issues. Although neither specifically addressed my particular problem, they did lead me to a workaround that solved everything. It turned out that the iTunes libraries that didn't show up on my iPhone or iPad had to be rebuilt.
To accomplish this, you need to quit iTunes and navigate to the Music Folder (/Users/[your username]/Music on the Mac; on Windows 7, the default location is \username\My Music\iTunes) where you'll find your iTunes folder. Open it up and look for two files: iTunes Library.xml and iTunes Library.
Drag the iTunes Library.xml file to your desktop and move the iTunes Library file to the trash. Then reopen iTunes; go to the File menu and choose Library->Import Playlist. A dialog box will open. Choose the iTunes Library.xml file that's on your desktop.
Depending upon the size of your iTunes library, you may have to wait a long time. Reloading all the content doesn't take all that long, but the "Determining Song Volume" part does. An 8,000 or so item library took over an hour to complete. The last step, and one that's easy to forget, is to go to the Advanced menubar option and turn Home Sharing back on. Go to your iDevice, run the iPod app, and under "Shared" all your rebuilt libraries will show up and be usable.
This has affected people using both iOS 4.3 and 4.3.1. I just installed iOS 4.3.2 and everything still works fine. Apple assures me this bug will be squashed in an upcoming software revision. If you have more than one Mac using Home Sharing, let us know if this bug has bitten you or if you came out unscathed. If you have PCs, tell us if this is a problem for you as well.
Note 4/15/11: I just found that in addition you'll need to enable all your iDevice sync preferences as well. I saw that all the settings has been disabled, and had to be turned back on. This is especially a pain since you'll have to decide once again which apps, music, etc., you want synced. You also have to resubscribe to your podcasts. However syncing without turning on anything won't delete any content from your iDevices.