Heya paddy_p,
It sounds like switching transients are inducing sufficient voltages on your inputs/interrupt lines to just cross over the input logic thresholds, erroneously fooling your micro into believing a desired signal transition has occurred. *Usually* these sort of problems can be made to go away with varying degrees of the following:
a) Make sure your micro has sufficient power supply decoupling, in the form of (at least) 100 nF right across the supply pins.
b) Ensure all unused inputs are pulled high/low as appropriate.
c) Make sure the RESET pin is driven appropriately, either by an RC network (with C > 10 nF) or a dedicated supervisory IC, and
d) If you have long input lines carrying low-bandwidth signals (such as to sensors/switches etc), these can potentially act as antennas for switching transients. Either:
* Electrically isolate them from the micro (by using optocouplers etc), or
* Add RC filters, with a series R in-line with the signal, and shunt C across the micro input. Naturally, adding an RC network will smear nice square edges into an exponential type slew, but provided the time constants aren't excessive (<10ms, say), your micro probably won't complain. Choose the largest time constant your circuit can tolerate (and still transmit the required data rate) for the best interference immunity.
E.g. For a burglar alarm with reed switches connected directly to the micro, a 1-10ms time constant would be entirely reasonable. Perhaps 10K and 100nF? An added bonus of RC networks on the inputs is that some degree of ESD protection can also be afforded by the addition of a transient suppressor or zener diode on the sensor side of the resistor to ground.
Hopefully that works for you!