First off, you need an air head in the HWT, and the easiest way to establish an air head in the tank is to simply turn off the pump, turn off the city water service, open the pressure/temperature relief valve and let it run until there is no water coming out. This lowers the water level to the valve level, thus leaving an air head in the tank. Turn on the city water or pump and let it fill the tank. Your head is re-established and there will be a very minimum of air in the water lines.
Now as to the continued drip. If you are operating your water heater as many LD'ers do, short cycling to get to temperature, then turning off until next time, you will probably always have the drip. This is due to the temperature differential in the tank vs. the valve and it's more condensation in the valve than leakage. If you read your water heater manual you will probably find this "NOTE" therein. You wish to install an adjustable thermostat.
If you are running the water heater in a continuous mode, i.e. turn it on and leave it on until you travel again, and you have a leak then you have a bad valve. It is possible to damage these valves during installation if you don't have the wrench that is designed for them. If you're using a pipe wrench or other wrench it helps to remove the burner shroud to the left of the valve and work gently, not torquing the valve too hard. They look tough, but there is a lot of hollow area in the valve.
It is especially important that when you have the valve open and are through doing whatever, let the lever snap closed. Don't be gentle with it or the seal will frequently not make up due to some "stuff" left on the seal. Just let it snap on it's own force. Once a year or so soak it in white vinegar.
Contributor: Mike Sylvester