Won't I get current flowing through the ground wires due to a difference in potential voltage?
Just want to clear up a thing or two about "potentials".
A potential only exist when it has got a reference.
So, if you pick a single line, no matter it's potential within its own loop, it doesn't have a potential at all.
You could even connect eg. +9V from one circuit with 0V/Gnd/Common from the other circuit, as long as there's only this line connecting them. You shouldn't however, as you'd get in trouble if you then connected a second line.
Just connect the 0V side of both supplies and you have common ground.
Also, I think I fried my servo today (started to smoke). I was measuring the current passing through the servo from the + and - terminals, and it seems to be pulling 2A even when not being driven by a signal from the microcontroller. I would assume that servos shouldn't do any work, and 2A*6V=12W of work for not doing anything seems a bit weird.
Perhaps you put the positive supply to the servo signal line or something similar.
You should consider using the terms positive (+) and Gnd/Common for 0V, as negative (-) is only used for... negative voltages.
If you use the negative pole of a battery for reference (eg. when measuring its voltage), this will be your 0V reference. If you use the positive pole for reference, this will be your Gnd and your battery will give only out negative voltages.