The screw that holds the agitator in place appeared to have worn and rusty threads. I tried to replace it with a standard hardware store 1/4-20 hex head screw but that wouldn't grip. I had thoughts of needing to tap the hole,but eventually bought the specified screw, which is a specialist. It has tapered threads, a shoulder, rubber bushings, an attached washer and a hex head. I spent a lot of time trying other things but when the real part arrived it only took a few minutes to set it in place.
BTW -- I never found a write-up anywhere on this specific issue.