I had a problem like that on my 02 Eddie Bauer. It will display "ajar door" with all the doors closed. This is what I did to solve the problem:
1. I activated the alarm and waited about 30 seconds then open one door only (this includes the liftgate and the rearglass window). If the alarm went off that meant that door was ok. Turn off the alarm and rearmed again to repeat the step. If no door/liftgate/rearglass sounded the alarm, you probably have a problem not related to the switches on the doors.
2. Once I found the door that did not sounded the alarm, I checked the wires in the grommet between the door and frame. You want to look for pinched or cut wires. If any damage is found it should be repaired.
3. If not damaged wires were found, I then moved to removed the door panel and looked for damaged wires inside the door. The ajar switch is part of the door lock actuator and latch. Is alltogether in an assembly. The assembly is hold by 3 screws and two rods. The screws you could access from the outside of the latch. The rods are hold in place by plastic clips (very fragile plastic clips).
4. This assembly has two electric plugs one for the lock actuator (the biggest of the two) and another for the ajar switch. If you disconnect the smaller plug and jump a wire between the two connectors inside the plug (make sure the jumper wire is making good contact) your "ajar door" display should turn off. If it does you need another switch (about $25 at a Ford dealer).
5. If your "ajar door" display does stay on you have a problem with the wiring/module somewhere else and just to be sure go over from step 1 again.
There was another post around here in which someone said to spray wd40 through the outside door handle. The ajar switch is to far down below the door for the spray to do anything. The best way to try and clean the switch is by removing the door panel spray directly on the switch. Imo it will be better just to get another one and replace it. The switch by itself is sealed, I dont see how it could be cleaned.
Feel free guys to add more info to this post. I spent a few hours trying to fix this thing and figuring everything out.
Orlando