I replaced that item, it's known as a wig-wag by the local appliance dealer, on my washer. The following week the transmission gave out. So it was new washer time since the of a transmission is almost that of a new washer.
I have book on fixing appliances and it's saved me much money over the years.
BTW, the correct screw to hold the points has a captive washer IIRC, and would not be too long even if the washer fell off. I suspect the culprit screw is a replacement. I have seen cases of a screw too long used to hold the capacitor to the side of the distributor, but that only made noise not destruction.