Q: The vehicle alarm is going off randomly. on 2005 Mercury Mariner

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The info window shows the right rear door is ajar when it is not. The yellow seatbelt light on the dash is also randomly appearing. Yesterday, the alarm activated while my wife was driving down the interstate even.
(3) Answers
I have a shop in Brownsburg, Indiana and had this problem not to long ago with another Ford. Wetry is correct on it is more than likely a BCM (Body Control Module) problem IF the alarm is factory istalled. Ford has many problems with contamination of BCMs and fuse boxes getting water and subsequent corrosion on them. Unforunately the easiest test(s) that can be ran on this vehicle involves a fairly expensive scan tool. This makes it a very simple diagnosis even if no codes. If you have access to one or even for your own knowledge whomever is looking at the live data for the BCM should look at system voltage. If faulty its almost always going to have an off the wall battery voltage reading. EX-22 volts. Really anything that isnt 12.4-14.2 on a constant basis. Thanks!
The body control module can be scanned for trouble codes.
Have this done and it should help with diagnosis. IF factory