It could be faulty wiring or a bad sensor. It could also be a problem with installation. Is it embedded in the door? The door sensor itself could be pushed to far into the hole. It could also be a problem with the door alignment not matching up perfectly. Many times, dark doors can warp...
Your motion detectors going off when the alarm is not enabled is a completely different issue. If you are talking about the motion detector light blinking because it notices movement, that is a good thing. If you are talking about your alarm going off out of the blue, you have a more serious...