Problem is more likely that your circuit is too high-impendance and susceptible to all kinds of pick.
I just checked the schematic of an Arduino Uno, and there are no pullups/pulldowns on the I/O pins, meaning that you are relying on the internal 50 kohm pullups.
This is far too high. In an appliance environment, you need to pull a few mA at least through the circuit for reliable signalling.
Try adding pullups at the inputs to the Arduino, forcing this current through the switch loops.
Start with 2 kohm pullups and take it from there.
Yeah, I know, bye-bye low-power design, but that's the way of the world :-)