inconsistent temperature readings (LM35DT)

How do you have the sensor ground pins connected? Post a photo of your setup.

For accurate results, the sensor ground pins should be connected to one of the GND pins on the Arduino, and anything else that needs to be connected to ground (apart from other sensors with analog output) should be connected to a different GND pin. This is especially important if the Arduino is controlling something that takes a lot of current. Otherwise, current flowing through the shared ground wire and connections induces a voltage across them, which affects the readings.