I believe I have resolved the issue by resetting my phone to factory defaults. After resetting to factory default, I am no longer experiencing the mysterious pauses when playing music.
My rev. 1 Moto DROID came loaded with Android 2.1. I ran the OTA update to 2.2, and then the OTA update to 2.2.1. In addition to the music playback issue, I was also experiencing extreme delays when displaying the launcher after the phone had been in a dockextreme delays when displaying the launcher after the phone had been in a dock. I hadn't performed a factory reset since loading the two OTA updates, so I went through the factory reset process. The home screen now displays much, much more quickly when removing the phone from a dock, and I have not experienced the music pause issue.