No, the neutral and ground should never be wired together. This is wrong, and potentially dangerous.
When you plug in something in the outlet, the neutral will be live, as it closes the circuit. If the ground is wired to the neutral, the ground of the applicance will also be live. This can be felt as a tingling if you touch the grounded casing of the appliance, because most of the current still goes through the neutral where the lowest resistance is.
However, if there is something wrong and the neutral is disconnected, it will make the appliance dangerous. If you touch the casing, and some real ground (like a water pipe) at the same time, you will close the circuit and carry all of the current.
So, connecting the ground to neutral totally defeats the purpose of having a ground, and actually makes it more dangerous than not having the ground at all.
When the inspector was measuring the ground, he was actually measuring the neutral, which naturally shows a current when something is connected somewhere in the circuit.