Some of the most common signs of ECT failure are a warm running motor, less than stellar gas milage, and soot at the tail pipes.
Many times when the ECT fails, the computer thinks the car is cooler than it actually is. Because of this, the computer goes into warm-up mode and dumps more fuel into the motor. The fan is so delayed, that the car gets extremely close to overheating before it starts to cool.
If your car is running warm('N' or above) and your fan does not seem to come on, turn on the AC to activate the fan. If it comes on and your water temperature goes down, you may have a bad ECT.
The ECT is located just to the right (or behind) the thermostat.