Like duranged03 said, it sounds like it might be a broken/damaged wire in the boot. Could be the switch or the mirror motor. When I get home tonight I will post the wiring diagram for the power mirrors to help you out in the troubleshooting process.
In the meantime:
I had similar electrical issues with my 02 xlt. The dome lights would stay on until the battery saver feature turned them off, the accessory delay wasn't working, the driver side puddle light didn't work, the keypad on the door would set off the alarm when I pressed it, the door ajar light would flash and beep at highway speeds, the radio would shut off as soon as I turned the key off, the delayed accessories didn't work, etc. The alarm would beep twice when I armed it. Recently all 4 windows stopped working. Most recently the driver door lock actuator stopped working.
A lot of electrical issues can be traced back to broken/damaged wire(s) in the boot between the body and the driver's door. I found 3 broken wires and repaired them. The thin black ground wire was broken and after repairing it all was back to normal. When the windows stopped working, I repaired the thick black ground wire and the windows now work like a champ. I had to repair the pink/black wire to fix the driver door lock actuator.
Here is the thread for removing the door panel:
http://www.explorerforum.com/forums//showthread.php?t=303524
Here is a great thread for checking for broken/damaged wires, thanks to
synyster for this awesome write-up:
http://www.explorerforum.com/forums//showthread.php?t=270081
Be sure to take your time when looking for broken/damaged wire(s). Check all the wires for breaks/damage. When you think you're done looking, look again, and again, and again. A bright flashlight can be very helpful.
Hope this helps out!! :biggthump
