Our washer has the older style control that has a mechanical timer on the switch instead of any computer board. It goes through the full cycles but does not spin out enough of the water. It also seems to be out of balance a lot and shakes a lot in the spin cycles. I am wondering what parts should be replaced.
Spin problems in these models can generally be fixed with this part here,
but the out of balance would still be an issue. After you replace the thrust bearing operate it with the front panel off and see if you can determine if there is a broken support structure piece or bad spring.