I can't think of anything that would cause this. The really strange part is that the space heater sometimes responds to the lighting commands. I take it the space heater has its own IR receiver independent of the MSC-400?
My only other thought is that a space heater draws a tremendous amount of current. It could be dipping the voltage on the line when it turns on. It probably throws out quite a bit of RF interference when turning on and off too. Any chance you could plug the space heater into a different circuit and see if it affects anything?