Ahh I see. I'll make sure to do it that way in the future. Thank you both for the tip/clarification.

Unfortunately this particular circuit is already on a PCB and it's too late to redesign.

I've been doing some reading about pull-ups. Someone mentioned that the weak internal pull-ups in the PIC24 family are about 50K and they could easily allow EMI on long traces (let alone external wires). I guess this means the 100K resistors are way out. Quite a few people use 10Ks but it seems that 5K is recommended so I'll give some of those a go later.

The good news is that the circuit has now been running for over 7 hours and hasn't randomly triggered once. Maybe the interference is coming from something that's only on at night.