I found this tidbit of information in the APM Manual under "LED Behavior". Does this bug still exist in current versions of the Beta code? If so, perhaps hitting the reset button after my MediaTek LED goes solid will fix my GPS problem?
Note: in the 1.0 Beta code there is a slight bug in the MediaTek setup routine, which requires you to reset your board after a cold start before the GPS lock will be registered. So if you're using the MediaTek GPS, wait until the blue lock LED on that module goes solid, then press the reset button on your APM board or shield. This will do a warm start of the board, and the LED behavior should be as shown in the table above.