The glitch stems from the software's Visual Voicemail audio source feature, which lets users choose whether they would like to play back their voicemail messages via the iPhone's earpiece, speaker, or wirelessly-connected Bluetooth headset.
For whatever reason, version 1.1.1 of the iPhone software released this week (as well as earlier versions) fails to disconnect the wireless audio stream from Bluetooth headsets when a user leaves the Visual Voicemail interface. It will instead continue to stream all of the phone's audio feedback — including keyboard clicks, shutter sounds, and music tracks — to the wireless headsets.
How to get it working
To take advantage of the bug and begin streaming music wirelessly, simply initiate a connection between your Bluetooth headset and the iPhone. Once the iPhone recognizes a connection from your paired headset, enter the Visual Voicemail interface under the phone application and select the "Audio" button from the upper right-hand corner of the screen. (If you do not have a Bluetooth headset paired to the iPhone or your Bluetooth headset has not initiated a connection with the iPhone, this button will instead say "Speaker".)
You should now have the option to "Change audio source" to either "iPhone Bluetooth Headset," "iPhone," or "Speaker Phone." Choose the first one. That's about it. You should now be able to navigate to your iPhone's iPod application and begin streaming music to your headset. Similarly, entering the SMS or Safari applications will continue to stream audio — such as keyboard clicks — in the same manner.
Obviously, the usefulness of this jury-rigged solution is somewhat questionable given that the iPhone will continue to simultaneously output the same audio through its built-in speaker. If you plug headphones into the iPhone in an attempt silence the speaker, it will cut the wireless connection to your headset. However, once disconnect the headphones, the iPhone will resume the wireless audio stream.