Yes, there are certain reading values that are good indicators of problems:
Reading of 12000 in either axis: This indicates a sensor problem.
Reading of ±6000 to 8000: This indicates a power line problem if it appears both axes. The problem is probably in the cable or a connector.
Reading of +730 or 740 (English) or +1280 or 1290 (Metric): This indicates an input line problem on DataMates with firmware version 1997 or earlier. This is the same reading that appears if no probe is connected. The problem is probably in the cable or a connector.
Reading of +1786 or 1787 (English) or +3125 or 3126 (Metric): This indicates an input line problem on DataMates with firmware 2005 or later. This is the same reading that appears if no probe is connected. The problem is probably in the cable or a connector.
Reading of 60 or some other low number: If you see a low number that stays constant in one axis, the problem is mostly likely in the probe. The accelerometer for that axis is not working and the op amp is trying to compensate, resulting in a constant value.