I have the exact same problem on my single spray-arm GE GSD500D. Last couple years or so, the spray arm has moved very slowly, although spray water is coming out like gangbusters. Shoots to the kitchen ceiling if I turn it on with door open! Lately it doesn’t move at all. Last year I checked everything around the filter area and it seemed okay & unclogged. The spray arm hub wobbles somewhat, but it does on new dishwashers I have looked at! I did try last year to shim under the screw that holds the hub to the pump housing and it seemed to help but not much.
I have begun shopping for a new dishwasher but if I can fix this inexpensively and milk another year or so out of this dinosaur (we may be selling & moving due to low interest rates) it would be nice.
Doug in Southern Cal.