While replacing a light switch, I shut off the circuit breaker for it and checked the voltage to be sure it was not hot. I noticed that the hot wire read 10VAC, which was odd. It was pretty consistent. Just on a hunch, I went and shut off the circuit breaker for another circuit nearby (the GFCI circuit for the bathroom outlets) and the 10 VAC went away.
I checked the neutral wire resistance to ground, and it was very low, which is correct.
Any ideas on what to look at for this?