Suppose I have an Arduino in my living room and a 50' wire to a doorbell type swich, normally open.
Are there any steps I can take to protect the Arduino from "seeing" false switch closures arising from voltages induced in that long wire (read "antenna") when big motors around the house (heating pump, refrigerator) throw out "noise"?
Are there any steps I can take to protect the Arduino
Yes
http://www.thebox.myzen.co.uk/Tutorial/Protection.html
Also adding capacitors at the arduino end can help. Also consider using the analogue input to detect the push switch. That way you can set your own thresholds instead of having them set for you by the digital input pins.
Use the same noise-suppression technique seen in rs-422 wiring that makes it superior to rs-232 wiring.
You could decrease the value of your pullup/pulldown resistor. Hold the sucker high or low by brute force and ignorance....... 