I finally got around to upgrading to Flex Builder 3.0.2 (and the new 3.2 SDK!). After the upgrade, however, I couldn't run my AIR project in the in the AIR debugger :(
Flex Builder displayed an error dialog showing the command it used to debug my app, and it's resulting output: "error while loading initial content".
Fortunately, as described in this JIRA bug, the solution was simple. Update the namespace in your AIR project's AppName-app.xml file to reflect the new AIR version 1.5: