Why is there a 66 Vac reading on the metal shield of our AC socket?
I've seen this happen before.

First: I have to make a couple of assumptions because you didn't include enough information in your question.

I'm assuming that you have a nominal 120 Vac AC Mains supply.

Where I have seen this before is when your outlet is connected to the supply with standard Loomex / Romex 14/2 wire with ground conductor.  

The problem is that the ground conductor in the cable is not connected at the source.

The AC voltage that you measured is coming from the capacitive coupling between the AC Hot and Neutral.  Because the ground is about the same distance between each of the insulated conductors, there is about the same amount of capacitance from each of the conductors to the ground wire.  This looks like an approximate 2:1 capacitive voltage divider.

The amount of current that you are measuring says that there is a fair amount of capacitance between the ground wire and the main conductors.  That means that the ground is broken / disconnected quite some distance away from the socket.

If the ground was disconnected right at the AC socket, the voltage wouldn't be quite in the middle like it is now and you wouldn't have that much current flowing when you do the current measurement.

Regardless, this is a dangerous situation and needs to be fixed.

If you can't find the broken or disconnected ground wire, run a separate ground wire from the outlet socket to the cold-water pipe that you used during your testing.  Ideally, you would take your ground from the cold-water pipe right when it comes into your building, BEFORE the water meter or shut-off valve.