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 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
Unfortunately the pictures are no longer available in the above thread. IIRC, I believe I unwrapped the wires enough to gain access. When I have gone searching in there I had an idea of what wire I was looking for. I located the the wire I was looking for and gently tugged on that wire on the door side. The wire was pulled toward me and out of the harness. I then went inside the vehicle and gently tugged on the the wire I was looking for and was able to pull it inside the vehicle. I then spliced a length of wire to the 2 ends, completing the circuit. I then gently pulled the excess into the door.
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.
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Could also be related to the door ajar switch.
Here is a great thread for checking/replacing the door ajar switch, thanks to
borland for the awesome write-up:
http://www.explorerforum.com/forums/showthread.php?t=249253
That is a great write up.
On a side note, before going through a complete replacement of the switch, you can spray WD40 into the door latch opening on each door, as these become stuck sometimes....and this can alleviate the issue.
This worked for me, after going for more than a year of the "door ajar" light coming on occasionally...mainly after a car wash, high humidity, or rain....making me unable to lock/arm the vehicle from the door keypad and keeping the dome lights on. Worth a try....it worked for me
The red arrows show you where to spray:
Good luck getting it sorted.
Please keep us posted as feedback helps others reading this post looking for a fix to the same or similar issue! 
