After i shut all the doors in the montero i have (1998) the door open light in the dash is always on i check all the doors the tail gate and the hood... it only shuts off when i have the alarm on..2nd idk if its the motor or a gear but my passanger side wiper works but not the passanger....it stays where it is..

 

Put your hand on the broken wiper and feel if the motor in it is even TRYING to turn the wiper, thatll clear up any confusion as to what it is... My guess? A loose connection. Ive never really seen too many wiper motors go completely bad. It may have spun through the teeth on the wiper arm, that Ive seen... As for your doors, its more than likely that one of the little switches that shut off that light (contained in every door frame) has gone bad. Try (one at a time) pressing them down manually with your finger to see which one it may be.

 

my guess on the wiper is either a connection, or it could just be that the wiper isnt bolted in correctly. Remove the wiper at the bolt and see if the part is turning. Or just see if its loose