The Tiger Mail problems I was having appear to be resolved.
I removed the Library -> Preferences folder and re-started the Mac.
Then I added the com.apple.mail.plist file back in to the new Preferences folder and checked my Mail. The issues which had been plagueing me didn’t recur – wahoo!
I added back in a couple of preference files from the old Preferences folder (like com.apple.finder.plist, com.apple.desktop.plist, etc.) and so far, everything seems to be going well.