I have licenced electrician to install separate panel with five dedicated lines connected to it:
A sub panel fed from the main electrical panel.
By chance do you know what size wire he used to feed the sub panel?
I assume the electrician fed the sub panel from a 2 pole breaker in the main panel. Look on the breaker handle of the breaker what is the number? 40, 50,60, ect?
Because you have a sub panel the panel will have a separate ground bar. The equipment grounding conductors that are part of the dedicated branch circuits that feed the receptacles will terminate on this bar. The ground bar will have an equipment grounding conductor, wire, that goes backs and connects to the main electrical panel ground bar. No exception....per NEC.
He used Romex 12/3 wire, and to my understanding, at least, that's how I asked him to do it, ground wire from each receptacle (actually there are two receptacles on each run of wire)......
A dedicated circuit feeds two duplex receptacles? Is that correct?
Why did you use 12/3 with ground? Is the ground bar in the sub panel an isolated ground bar? There by isolated from the panel's metal enclosure?
...... is connected to a ground bar in the panel, and the ground bar is connected to a copper ground rod right next to the panel, and to a common house ground elsewere.
More than likely here is your problem. Just bet you have a difference of potential, voltage, between the equipment ground at the receptacles and the neutral, the grounded conductor.
Per NEC the feeder equipment grounding conductor shall be installed in the same cable, or raceway, as the feeder current carrying conductors. And the equipment grounding conductor shall terminate in the same panel the feeder is fed from.
http://www.aes.org/sections/pnw/pnwrecaps/2005/whitlock/whitlock_pnw05.pdf