The glass sensor could fail to communicate with the sensor control panel, which sets off the alert that glass has been broken in the house. This is especially dangerous, since an intruder can now enter undetected.
If you happen to drop and break a heavy glass object within the range of the sensors, like a vase or a mirror, the ADT system will think someone has broken in because it's sensed the vibration of the breaking glass and sound the alarm.
Someone who has an ADT system installed in their apartment could have their sensors triggered if a window or other glass item is broken in a nearby unit. This problem could also occur in a neighborhood where houses are situated very close together.