You need Java 1.6 for Mac OS 10.6 update 16. To install, got to launch System Preferences and click on Software Update and click on Check Now. All uncheck everything except Java and click to install. Minecraft is up and running for me now.
In addition to the above, I also tried 1.5.2 and 1.5.1 with the new launcher without success. The error message is unchanged.
I also deleted Minecraft.app and ~/Library/Application Support/minecraft and reinstalled without success.
You need Java 1.6 for Mac OS 10.6 update 16. To install, got to launch System Preferences and click on Software Update and click on Check Now. All uncheck everything except Java and click to install. Minecraft is up and running for me now.