I am plugged into a surge protector, and actually, both arduino boards that I'm testing with are plugged into laptops, so the boards shouldn't be seeing surges.
As for the doorbell, I have the AC from the doorbell going through a bridge rectifier and voltage regulator to pull the coil on a 5v relay. In the tests i've done, I've had doorbell presses change the pinstate for anywhere from 10ms to 1s depending on how long the doorbell is pressed - longer if you hold the doorbell of course. I know I can "debounce" both the hardware and the code to solve this, but I still don't feel comfortable with that. Nothing outside of the circuit should cause the pin to change state. As mentioned above, this doesn't fix the problem, it just circumvents it.
As for millis debouncing, the millis counter cycles back to 0 over time, correct? That won't work, since this will be running permanently.
Since unplugging the fridge, I have not had any issues. When I get home tonight, I am going to plug the refridgerator into a different ciruit. But leave it sitting where it is. I'm curious what will happen.