trigger on 1) intermittent loss of the 240vac coil voltage
before that contactor you have some trigger device (relay, pcb, whatever), if you 'scope' that contact or transistor (when he's closed, you have the coil powered, when it's opened you have contactor not powered), so it's simple to trigger that device (you have small voltage for contactor coil ON and high for OFF)
for the 2'nd, in your place i'll use some calculated resistor on one relay contact, here you get voltage when contactor opens his contacts for whatever reason like coil not energised or bad contact, BUT the oscilloscope probe voltage capabilities must be respected, maybe use a separation transformer. the load AFTER the contactor contacts is energised via your monitoring load for contactor switch, so maybe you should disconnect the contactor load just to filter what you want, if it's coil or contact problem. of course if you disconnect the contactor load(s) you can connect some test load like a light bulb, and that in conjunction with the resistor test load will give you what you need to trigger. hope you get the schematic idea.
i know, everybody says the separation must be on DUT side, you're a beginner, so be advised. i use sometimes on the oscilloscope side, but i take care not to fry my precious hands

because you can get mains power on oscilloscope ground clip for example